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A027040 a(n) = self-convolution of row n of array T given by A027023. 2
1, 3, 9, 31, 129, 531, 2129, 8351, 32177, 122211, 458801, 1706015, 6293169, 23057651, 83992313, 304424639, 1098525761, 3948727555, 14145206209, 50515602111, 179904080257, 639103899411, 2265253438745, 8012421964063 (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_{k=0..2*n} T(n,k)*T(n,2*n-k), where T = A027023. - G. C. Greubel, Nov 05 2019

MAPLE

T:= proc(n, k) option remember;

      if (n<0 or k>2*n) then 0

    elif k<3 or k=2*n then 1

    else add(T(n-1, k-j), j=1..3)

      fi

    end:

seq( add(T(n, k)*T(n, 2*n-k), k=0..2*n), n=0..30); # G. C. Greubel, Nov 05 2019

MATHEMATICA

T[n_, k_]:= T[n, k]= If[n<0 || k>2*n, 0, If[k<3 || k==2*n, 1, Sum[T[n-1, k-j], {j, 3}]]]; Table[Sum[T[n, k]*T[n, 2*n-k], {k, 0, 2*n}], {n, 0, 30}] (* G. C. Greubel, Nov 05 2019 *)

PROG

(Sage)

@CachedFunction

def T(n, k):

    if (n<0 or k>2*n): return 0

    elif (k<3 or k==2*n): return 1

    else: return sum(T(n-1, k-j) for j in (1..3))

[sum(T(n, k)*T(n, 2*n-k) for k in (0..2*n)) for n in (4..30)] # G. C. Greubel, Nov 05 2019

CROSSREFS

Sequence in context: A182968 A071603 A090595 * A111063 A245116 A255382

Adjacent sequences:  A027037 A027038 A027039 * A027041 A027042 A027043

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified April 22 19:11 EDT 2021. Contains 343177 sequences. (Running on oeis4.)