1,2

Comment from David W. Wilson: Numbers triangular, differences square.

Partial sums of A001019. This is m-th triangular number, where m is partial sums of A000244. a(n)=A000217(A003462(n)). - Lekraj Beedassy (blekraj(AT)yahoo.com), May 25 2004

With offset 0, binomial transform of A003951 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 22 2005

Numbers in base 9: 1, 11, 111, 1111, 11111, 111111,1111111, etc. [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2009]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 112.

J. Riordan, Combinatorial Identities, Wiley, 1968, p. 217.

T. N. Thiele, Interpolationsrechnung. Teubner, Leipzig, 1909, p. 36.

M. Ward, Note on divisibility sequences, Bull. Amer. Math. Soc., 42 (1936), 843-845.

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Index entries for sequences related to linear recurrences with constant coefficients

a(n) = 9*a(n-1) + 1; a(1) = 1 . G.f.: x / ((1-x)*(1-9*x)) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Mar 13 2004

a:=n->sum(9^(n-j), j=1..n): seq(a(n), n=1..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 04 2007

A002452:=1/(9*z-1)/(z-1); [S. Plouffe in his 1992 dissertation.]

lst={}; Do[p=(9^n-1)/8; AppendTo[lst, p], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 29 2008]

(Other) sage: [lucas_number1(n, 10, 9) for n in xrange(1, 20)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2009]

(Other) sage: [gaussian_binomial(n, 1, 9) for n in xrange(1, 20)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 28 2009]

(Other) sage: [gaussian_binomial(2*n, 1, 3)/4 for n in xrange(1, 20)] # [From Zerinvary Lajosz (zerinvarylajos(AT)yahoo.com), May 28 2009]

Right-hand column 1 in triangle A008958.

Sequence in context: A143572 A002739 A079928 this_sequence A096261 A015455 A110410

Adjacent sequences: A002449 A002450 A002451 this_sequence A002453 A002454 A002455

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Pab Ter (pabrlos(AT)yahoo.com), May 08 2004