A210695 a(n) = 6*a(n-1) - a(n-2) + 6 with n>1, a(0)=0, a(1)=1.

0, 1, 12, 77, 456, 2665, 15540, 90581, 527952, 3077137, 17934876, 104532125, 609257880, 3551015161, 20696833092, 120629983397, 703083067296, 4097868420385, 23884127455020, 139206896309741, 811357250403432, 4728936606110857, 27562262386261716

Offset: 0

Author

Kenneth J Ramsey, May 09 2012

Keywords

• nonn
• easy

Comments

It appears that if p is a prime of the form 8*r +/- 1, a(p-1) == 0 (mod p); and that if p is a prime of the form 8*r +/- 3, a(p+1) == 0 (mod p).

Links

• Bruno Berselli, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (7,-7,1).

Crossrefs

Cf. A054490 (first differences).

Programs

Magma

[n le 2 select n-1 else 6*Self(n-1)-Self(n-2)+6: n in [1..23]]; // Bruno Berselli, Jun 26 2012

Mathematica

m = 36;n = 5; c = 0;
list3 = Reap[While[c < 22, t = 6 n - m + 6; Sow[t];m = n; n = t;c++]][[2,1]]

Formula

G.f.: x*(1+5*x)/((1-x)*(1-6*x+x^2)). [Bruno Berselli, Jun 26 2012]

a(n) = ((1-2*sqrt(2))*(1-sqrt(2))^(2n-1)+(1+2*sqrt(2))*(1+sqrt(2))^(2n-1)-6)/4. [Bruno Berselli, Jun 26 2012]

2*a(n) = 3*A001109(n+1)-13*A001109(n)-3. - R. J. Mathar, Jul 18 2012

Extensions

Definition rewritten from Bruno Berselli, Jun 26 2012