A102785 G.f.: (x-1)/(-2*x^2 + 3*x^3 + 2*x - 1).

1, 1, 0, 1, 5, 8, 9, 17, 40, 73, 117, 208, 401, 737, 1296, 2321, 4261, 7768, 13977, 25201, 45752, 83033, 150165, 271520, 491809, 891073, 1613088, 2919457, 5285957, 9572264, 17330985, 31375313, 56805448

Offset

0,5

Comments

Inverse binomial transform of A078017. Inversion of A052102.

Floretion Algebra Multiplication Program, FAMP Code: 4jbasekseq[ (+ 'ii' + 'jj' + 'ij' + 'ji' + e)*x) ] where x is defined as 1/4 times the sum of all 16 floretion basis vectors.

Links

Table of n, a(n) for n=0..32.

Index entries for linear recurrences with constant coefficients, signature (2,-2,3).

Formula

a(n+3) = 2a(n+2) - 2a(n+1) + 3a(n), a(0) = 1, a(1) = 1, a(2) = 0

a(n) = Sum(k=1..n, Sum(i=k..n, (Sum(j=0..k, binomial(j,-3*k+2*j+i)*(-2)^(-3*k+2*j+i)*3^(k-j)*binomial(k,j)))*binomial(n+k-i-1,k-1))), n > 0, a(0)=1. - Vladimir Kruchinin, May 05 2011

Prog

(Maxima)
a(n):=sum(sum((sum(binomial(j, -3*k+2*j+i)*(-2)^(-3*k+2*j+i)*3^(k-j)*binomial(k, j), j, 0, k))*binomial(n+k-i-1, k-1), i, k, n), k, 1, n); /* Vladimir Kruchinin, May 05 2011 */
(Maxima) makelist(coeff(taylor((x-1)/(-2*x^2+3*x^3+2*x-1), x, 0, n), x, n), n, 0, 32); /* Bruno Berselli, May 30 2011 */

Crossrefs

Cf. A078017, A052102, A077952.

Sequence in context: A045221 A046287 A051220 * A260348 A276934 A127493

Adjacent sequences: A102782 A102783 A102784 * A102786 A102787 A102788

Keyword

nonn

Author

Creighton Dement, Feb 11 2005

Status

approved