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

Author

Creighton Dement, Feb 11 2005

Keywords

• nonn

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

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

Crossrefs

Cf. A078017, A052102, A077952.

Programs

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 */

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