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A051624 12-gonal numbers. +0
27
0, 1, 12, 33, 64, 105, 156, 217, 288, 369, 460, 561, 672, 793, 924, 1065, 1216, 1377, 1548, 1729, 1920, 2121, 2332, 2553, 2784, 3025, 3276, 3537, 3808, 4089, 4380, 4681, 4992, 5313, 5644, 5985, 6336, 6697, 7068, 7449, 7840, 8241, 8652 (list; graph; listen)
OFFSET

0,3

COMMENT

Zero followed by partial sums of A017281. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 20 2008]

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pps. 194-196.

L. Hogben, Choice and Chance by Cardpack and Chessboard. Vol. 1, Chanticleer Press, NY, 1950, p. 36.

Murray R. Spiegel, Calculus of Finite Differences and Difference Equations, "Schaum's Outline Series", McGraw-Hill, 1971, pps. 10-20, 79-94.

LINKS

T. D. Noe, Table of n, a(n) for n=0..1000

Index entries for sequences related to linear recurrences with constant coefficients

FORMULA

n*(5*n-4).

G.f.: x*(1+9*x)/(1-x)^3.

a(n) = Sum_{k=0..n-1} 10*k+1. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 20 2008]

a(n)=10*n+a(n-1)-19 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 12 2009]

EXAMPLE

For n=2, a(2)=10*2+0-19=1; n=3, a(3)=10*3+1-19=12; n=4, a(4)=10*4+12-19=33 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 12 2009]

MAPLE

a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=2*a[n-1]-a[n-2]+10 od: seq(a[n], n=0..42); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 18 2008

MATHEMATICA

s=0; lst={s}; Do[s+=n++ +1; AppendTo[lst, s], {n, 0, 6!, 10}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 15 2008]

PROGRAM

(MAGMA) [ n eq 1 select 0 else Self(n-1)+10*(n-2)+1: n in [1..43] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 20 2008]

CROSSREFS

First differences of A007587. Cf. A051682.

Cf. A093645 ((10, 1) Pascal, column m=2). Partial sums of A017281.

Cf. A000217, A051682, A051865.

Sequence in context: A079561 A131543 A063296 this_sequence A039338 A118337 A032604

Adjacent sequences: A051621 A051622 A051623 this_sequence A051625 A051626 A051627

KEYWORD

easy,nonn,new

AUTHOR

Barry E. Williams

EXTENSIONS

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 09 1999

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.


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