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A096977
a(n) = 4*a(n-1) + 3*a(n-2) - 14*a(n-3) + 8*a(n-4).
3
0, 1, 2, 11, 36, 157, 598, 2447, 9672, 38913, 155194, 621683, 2484908, 9943269, 39765790, 159077719, 636281744, 2545185225, 10180624386, 40722730555, 162890456180, 651562756781, 2606249162982, 10425000380191, 41699994064216
OFFSET
0,3
COMMENTS
Original name was: A Jacobsthal summation.
The convolution of A024000 and A003683. Inverse binomial transform is A055275, with interpolated zeros.
FORMULA
G.f.: x*(1-2*x)/((1-x)^2*(1+2*x)*(1-4*x)).
a(n) = 4*4^n/27 - 4*(-2)^n/27 + n/9.
a(n) = Sum_{k=0..n} A001045(k)^2.
a(n) = 4*a(n-1) + 3*a(n-2) - 14*a(n-3) + 8*a(n-4).
MATHEMATICA
LinearRecurrence[{4, 3, -14, 8}, {0, 1, 2, 11}, 30] (* Harvey P. Dale, Jul 01 2015 *)
PROG
(Magma) [4*4^n/27-4*(-2)^n/27+n/9: n in [0..30]]; // Vincenzo Librandi, Jul 01 2011
(PARI) a(n)=(4*4^n-4*(-2)^n+3*n)/27 \\ Charles R Greathouse IV, Jul 01 2011
CROSSREFS
Cf. A001654.
Sequence in context: A375500 A176916 A015519 * A353979 A084098 A263547
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jul 17 2004
STATUS
approved