0,2

Binomial transform is A109114 (Comment: Kekule numbers for certain benzenoids). Invert transform is A109115 (Comment: Kekule numbers for certain benzenoids.) Inverse invert transform is: A016777 (Comment: Ignoring the first term, this sequence represents the number of bonds in a hydrocarbon: a(#of carbon atoms)=number of bonds. - Nathan Savir (thoobik(AT)yahoo.com), Jul 03 2003.) Inverse binomial transform is A006130. Program "Superseeker" finds (incomplete): A052924(n+1) - A052924(n) = a(n). May be seen as a transform of the zero-sequence A000004 (see "force transforms" link).

Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 06 2008: (Start)

Equals right border of triangle A143972.

(1, 5, 16, 53, 175,...) = row sums of triangle A143972 and INVERT transform of A016777: (1, 4, 7, 10,...). (End)

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

G.f. (-2*x-1)/(x^2-1+3*x)

a(n)=-(7/26)*[3/2-(1/2)*sqrt(13)]^n*sqrt(13)+(7/26)*sqrt(13)*[3/2+(1/2)*sqrt(13)]^n+(1/2)*[3/2 -(1/2)*sqrt(13)]^n+(1/2)*[3/2+(1/2)*sqrt(13)]^n, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Sep 19 2008]

seriestolist(series((-2*x-1)/(x^2-1+3*x), x=0, 25)); -or- Floretion Algebra Multiplication Program, FAMP Code: 4ibaseforseq[ + .25'i + .25i' + 1.25'ii' + .25'jj' + .25'kk' + .25'jk' + .25'kj' + .25e], 1vesfor = A000004

with(combinat): a:=n->2*fibonacci(n-1, 3)+fibonacci(n, 3): seq(a(n), n=1..25); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 04 2008

Cf. A109114, A109115, A016777, A006130, A000004, A052924.

A143972, A016777 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 06 2008]

Sequence in context: A077840 A007343 A147536 this_sequence A041469 A089102 A098912

Adjacent sequences: A108297 A108298 A108299 this_sequence A108301 A108302 A108303

nonn

Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Jul 24 2005