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A117719 a(2n) = A001653(n) (Numbers n such that 2*n^2 - 1 is a square), a(2n+1) = A038725(n+1). 1
1, 2, 5, 11, 29, 64, 169, 373, 985, 2174, 5741, 12671, 33461, 73852, 195025, 430441, 1136689, 2508794, 6625109, 14622323, 38613965, 85225144, 225058681, 496728541, 1311738121, 2895146102, 7645370045, 16874148071, 44560482149 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
G.f.: (1+2*x-x^2-x^3)/((1-2*x-x^2)*(1+2*x-x^2)).
a(n) = (1/4)*( 3*P(n+1) + 2*P(n) + (-1)^n*P(n-1) ), where P(n) = A000129(n). - G. C. Greubel, Jul 23 2023
MATHEMATICA
LinearRecurrence[{0, 6, 0, -1}, {1, 2, 5, 11}, 40] (* G. C. Greubel, Jul 23 2023 *)
PROG
(Magma) I:= [1, 2, 5, 11]; [n le 4 select I[n] else 6*Self(n-2) -Self(n-4): n in [1..40]]; // G. C. Greubel, Jul 23 2023
(SageMath)
A000129=BinaryRecurrenceSequence(2, 1, 0, 1)
def A117719(n): return (3*A000129(n+1) +2*A000129(n) +(-1)^n*A000129(n-1))/4
[A117719(n) for n in range(41)] # G. C. Greubel, Jul 23 2023
CROSSREFS
Sequence in context: A040998 A215939 A309857 * A355516 A359661 A316769
KEYWORD
nonn,easy
AUTHOR
Creighton Dement, Apr 13 2006
STATUS
approved

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Last modified May 29 03:48 EDT 2024. Contains 372921 sequences. (Running on oeis4.)