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A210695
a(n) = 6*a(n-1) - a(n-2) + 6 with n>1, a(0)=0, a(1)=1.
2
0, 1, 12, 77, 456, 2665, 15540, 90581, 527952, 3077137, 17934876, 104532125, 609257880, 3551015161, 20696833092, 120629983397, 703083067296, 4097868420385, 23884127455020, 139206896309741, 811357250403432, 4728936606110857, 27562262386261716
OFFSET
0,3
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).
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
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]]
PROG
(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
CROSSREFS
Cf. A054490 (first differences).
Sequence in context: A266766 A026964 A026974 * A109711 A244390 A136540
KEYWORD
nonn,easy
AUTHOR
Kenneth J Ramsey, May 09 2012
EXTENSIONS
Definition rewritten from Bruno Berselli, Jun 26 2012
STATUS
approved