A027265 a(n) = Sum_{k=0..2n-3} T(n,k) * T(n,k+3), with T given by A026519.

24, 104, 954, 3786, 33648, 131264, 1159844, 4508580, 39809076, 154773696, 1367463642, 5323519838, 47082494816, 183586707648, 1625447736120, 6348284151024, 56265306436584, 220081449149440, 1952476424575980, 7647723960962932, 67907006619888744, 266322435212031984

Offset

3,1

Links

G. C. Greubel, Table of n, a(n) for n = 3..1000

Formula

a(n) = Sum_{k=0..2n-3} A026519(n,k) * A026519(n,k+3).

Mathematica

T[n_, k_]:= T[n, k]= If[k<0 || k>2*n, 0, If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[(n+1)/2], If[EvenQ[n], T[n-1, k-2] + T[n-1, k], T[n-1, k-1] + T[n-1, k-2] + T[n-1, k] ]]]]; (* T = A026519 *)
a[n_] := a[n] = Block[{$RecursionLimit = Infinity}, Sum[T[n, k]*T[n, k+3], {k, 0, 2*n-3}] ];
Table[a[n], {n, 3, 40}] (* G. C. Greubel, Dec 21 2021 *)

Prog

(Sage)
@CachedFunction
def T(n, k): # T = A026519
    if (k<0 or k>2*n): return 0
    elif (k==0 or k==2*n): return 1
    elif (k==1 or k==2*n-1): return (n+1)//2
    elif (n%2==0): return T(n-1, k) + T(n-1, k-2)
    else: return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
@CachedFunction
def a(n): return sum( T(n, k)*T(n, k+3) for k in (0..2*n-3) )
[a(n) for n in (3..40)] # G. C. Greubel, Dec 21 2021

Crossrefs

Cf. A026519, A026520, A026521, A026522, A026523, A026524, A026525, A026526, A026527, A026528, A026529, A026530, A026531, A026532, A026533, A026534, A027262, A027263, A027264, A027266.

Sequence in context: A186932 A275506 A185743 * A044275 A044656 A011199

Adjacent sequences: A027262 A027263 A027264 * A027266 A027267 A027268

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Sean A. Irvine, Oct 26 2019

Status

approved