A026021 - OEIS

A026021

a(n) = T(n, [n/2]), where T is the array defined in A026009.

1, 1, 2, 3, 6, 10, 19, 34, 62, 117, 207, 407, 704, 1430, 2431, 5070, 8502, 18122, 30056, 65246, 107236, 236436, 385662, 861764, 1396652, 3157325, 5088865, 11622015, 18642420, 42961470, 68624295, 159419670, 253706790, 593636670, 941630580, 2217608250, 3507232740

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..36.

FORMULA

Conjecture: -(n+7)*(5*n-34)*a(n) + 8*(-n-14)*a(n-1) + (27*n^2-83*n-428)*a(n-2) + 8*(4*n+5)*a(n-3) 44*(n-3)*(7*n-27)*a(n-4) = 0. - R. J. Mathar, Jun 20 2013

From Amiram Eldar, Oct 12 2025: (Start)

a(n) = binomial(n, floor(n/2)) - binomial(n, floor(n/2)-3).

a(n) ~ c * 2^(n+3/2) / (n^(3/2) * sqrt(Pi)), where c = 12 if n is odd, and c = 9 if n is even. (End)

MATHEMATICA

a[n_] := Binomial[n, Floor[n/2]] - Binomial[n, Floor[n/2] - 3]; Array[a, 35, 0] (* Amiram Eldar, Oct 12 2025 *)

CROSSREFS

Cf. A026009.

Sequence in context: A165920 A274160 A190501 * A374690 A291875 A227309

Adjacent sequences: A026018 A026019 A026020 * A026022 A026023 A026024

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

STATUS

approved