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A302329
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a(0)=1, a(1)=61; for n>1, a(n) = 62*a(n-1) - a(n-2).
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9
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1, 61, 3781, 234361, 14526601, 900414901, 55811197261, 3459393815281, 214426605350161, 13290990137894701, 823826961944121301, 51063980650397625961, 3165142973362708688281, 196187800367837541047461, 12160478479832564836254301, 753753477949251182306719201
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OFFSET
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0,2
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COMMENTS
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Centered hexagonal numbers (A003215) with index in A145607. Example: 35 is a member of A145607, therefore A003215(35) = 3781 is a term of this sequence.
Also, centered 10-gonal numbers (A062786) with index in A182432. Example: 28 is a member of A182432 and A062786(28) = 3781.
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LINKS
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Colin Barker, Table of n, a(n) for n = 0..500
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (62,-1).
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FORMULA
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G.f.: (1 - x)/(1 - 62*x + x^2).
a(n) = a(-1-n).
a(n) = cosh((2*n + 1)*arccosh(4))/4.
a(n) = ((4 + sqrt(15))^(2*n + 1) + 1/(4 + sqrt(15))^(2*n + 1))/8.
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MATHEMATICA
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LinearRecurrence[{62, -1}, {1, 61}, 20]
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PROG
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(PARI) x='x+O('x^99); Vec((1-x)/(1-62*x+x^2)) \\ Altug Alkan, Apr 06 2018
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CROSSREFS
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Cf. A003215, A145607; A062786, A182432.
Fourth row of the array A188646.
First bisection of A041449, A042859.
Similar sequences of the type cosh((2*n+1)*arccosh(k))/k: A000012 (k=1), A001570 (k=2), A077420 (k=3), this sequence (k=4), A302330 (k=5), A302331 (k=6), A302332 (k=7), A253880 (k=8).
Sequence in context: A209087 A207052 A207129 * A218286 A126434 A096544
Adjacent sequences: A302326 A302327 A302328 * A302330 A302331 A302332
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KEYWORD
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nonn,easy
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AUTHOR
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Bruno Berselli, Apr 05 2018
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STATUS
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approved
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