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A027272 Self-convolution of row n of array T given by A026552. 18
1, 3, 19, 58, 462, 1608, 13446, 48924, 417440, 1553940, 13409576, 50618184, 440013462, 1676640462, 14649846820, 56201554888, 492944907180, 1900789437276, 16721000706580, 64734185205960, 570792185166764, 2216888144737508, 19584623363041704, 76265067399850848 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = Sum_{k=0..2*n} A026552(n, k)*A026552(n, 2*n-k).
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]*T[n, 2*n-k], {k, 0, 2*n}]];
Table[a[n], {n, 0, 40}] (* G. C. Greubel, Dec 18 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)*T(n, 2*n-k) for k in (0..2*n) )
[a(n) for n in (0..40)] # G. C. Greubel, Dec 18 2021
CROSSREFS
Sequence in context: A134268 A322209 A088798 * A337648 A164132 A106875
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Sean A. Irvine, Oct 26 2019
STATUS
approved

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)