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A026564 a(n) = Sum_{j=0..n} T(n, j), where T is given by A026552. 8
1, 2, 6, 11, 33, 64, 191, 376, 1122, 2222, 6636, 13180, 39395, 78373, 234414, 466840, 1397034, 2784266, 8335242, 16620976, 49773018, 99291358, 297406884, 593484440, 1777995535, 3548969075, 10633840743, 21230215328, 63620551947 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = Sum_{j=0..n} A026552(n, j).

MATHEMATICA

T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[(n+2)/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=A026552 *)

a[n_]:= a[n]= Block[{$RecursionLimit = Infinity}, Sum[T[n, k], {k, 0, n}]];

Table[a[n], {n, 0, 40}] (* G. C. Greubel, Dec 19 2021 *)

PROG

(Sage)

@CachedFunction

def T(n, k): # T = A026552

    if (k==0 or k==2*n): return 1

    elif (k==1 or k==2*n-1): return (n+2)//2

    elif (n%2==0): return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)

    else: return T(n-1, k) + T(n-1, k-2)

@CachedFunction

def a(n): return sum( T(n, k) for k in (0..n) )

[a(n) for n in (0..40)] # G. C. Greubel, Dec 19 2021

CROSSREFS

Cf. A026552, A026553, A026554, A026555, A026556, A026557, A026558, A026559, A026560, A026563, A026566, A026567, A027272, A027273, A027274, A027275, A027276.

Sequence in context: A135048 A189319 A268501 * A243794 A318199 A242791

Adjacent sequences:  A026561 A026562 A026563 * A026565 A026566 A026567

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified October 3 17:49 EDT 2022. Contains 357237 sequences. (Running on oeis4.)