A026534 a(n) = Sum_{i=0..2*n} Sum_{j=0..n-1} A026519(j, i).

1, 4, 10, 28, 64, 172, 388, 1036, 2332, 6220, 13996, 37324, 83980, 223948, 503884, 1343692, 3023308, 8062156, 18139852, 48372940, 108839116, 290237644, 653034700, 1741425868, 3918208204, 10448555212, 23509249228, 62691331276

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,6,-6).

Formula

a(n) = Sum_{i=0..2*n} Sum_{j=0..n-1} A026519(j, i).

G.f.: x*(1+3*x)/((1-x)*(1-6*x^2)). - Ralf Stephan, Feb 03 2004

a(n) = (1/60)*( 6^((n+1)/2)*( (4*sqrt(6) - 9)*(-1)^n + (4*sqrt(6) + 9) ) - 48 ). - G. C. Greubel, Dec 20 2021

Mathematica

LinearRecurrence[{1, 6, -6}, {1, 4, 10}, 40] (* G. C. Greubel, Dec 20 2021 *)

Prog

(Magma) I:=[1, 4, 10]; [n le 3 select I[n] else Self(n-1) +6*Self(n-2) -6*Self(n-3): n in [1..40]]; // G. C. Greubel, Dec 20 2021
(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( sum( T(j, i) for i in (0..2*n) ) for j in (0..n-1) )
[a(n) for n in (1..40)]
(PARI) Vec((1+3*x)/((1-x)*(1-6*x^2))+O(x^99)) \\ Charles R Greathouse IV, Jan 24 2022

Crossrefs

Cf. A026519, A026520, A026521, A026522, A026523, A026524, A026525, A026526, A026527, A026528, A026529, A026530, A026531, A026533, A027262, A027263, A027264, A027265, A027266.

Cf. A026532, A026551.

Sequence in context: A340568 A038579 A133726 * A034920 A274597 A335548

Adjacent sequences: A026531 A026532 A026533 * A026535 A026536 A026537

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved