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

Author

Clark Kimberling

Keywords

• nonn
• easy

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).

Crossrefs

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

Cf. A026532, A026551.

Programs

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

Mathematica

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

PARI

Vec((1+3*x)/((1-x)*(1-6*x^2))+O(x^99)) \\ Charles R Greathouse IV, Jan 24 2022

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)]

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