A084150 A Pell related sequence.

0, 0, 1, 3, 14, 50, 199, 749, 2892, 11028, 42301, 161799, 619706, 2372006, 9081955, 34767953, 133109592, 509594856, 1950956857, 7469077707, 28594853414, 109473250778, 419110475455, 1604533706357, 6142840740900, 23517417426300

Offset

0,4

Comments

Binomial transform of expansion of (sinh(sqrt(2)x))^2/4 = (0, 0, 1, 0, 8, 0, 64, ...). Inverse binomial transform of A006668.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,5,-7).

Formula

a(n) = ( (1+sqrt(8))^n + (1-sqrt(8))^n - 2 )/16.

E.g.f.: (1/4)*exp(x)*( sinh(sqrt(2)*x) )^2.

G.f.: x^2 / ( (1-x)*(1-2*x-7*x^2) ). - R. J. Mathar, Feb 05 2011

a(n) = (A015519(n) - A015519(n-1) - 1)/8 = (A084058(n) - 1)/8. - G. C. Greubel, Oct 11 2022

Mathematica

LinearRecurrence[{3, 5, -7}, {0, 0, 1}, 41] (* G. C. Greubel, Oct 11 2022 *)

Prog

(Magma) [n le 3 select Floor((n-1)/2) else 3*Self(n-1) +5*Self(n-2) -7*Self(n-3): n in [1..41]]; // G. C. Greubel, Oct 11 2022
(SageMath)
A084058 = BinaryRecurrenceSequence(2, 7, 1, 1)
def A084150(n): return (A084058(n) - 1)/8
[A084150(n) for n in range(41)] # G. C. Greubel, Oct 11 2022

Crossrefs

Cf. A006646, A006668, A015519, A084058.

Sequence in context: A187917 A164304 A098521 * A203196 A359253 A320826

Adjacent sequences: A084147 A084148 A084149 * A084151 A084152 A084153

Keyword

easy,nonn

Author

Paul Barry, May 16 2003

Status

approved