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A084150 A Pell related sequence. 2
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..25.

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. : exp(x)(sinh(sqrt(2)x))^2/4.

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

MATHEMATICA

Join[{a=0, b=0}, Table[c=2*b+7*a+1; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 05 2011*)

CROSSREFS

Cf. A006646.

Sequence in context: A187917 A164304 A098521 * A203196 A320826 A322199

Adjacent sequences:  A084147 A084148 A084149 * A084151 A084152 A084153

KEYWORD

easy,nonn

AUTHOR

Paul Barry, May 16 2003

STATUS

approved

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Last modified May 7 23:48 EDT 2021. Contains 343652 sequences. (Running on oeis4.)