OFFSET
1,5
REFERENCES
TERMESZET VILAGA XI.TERMESZET-TUDOMANY DIAKPALYAZAT 133.EVF. 6.SZ. jun. 2002. Vegh Lea (and Vegh Erika): "Pascal-tipusu haromszogek" http://www.kfki.hu/chemonet/TermVil/tv2002/tv0206/tartalom.html
LINKS
G. C. Greubel, Rows n = 1..100 of triangle, flattened
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 6, 1;
1, 16, 26, 1;
1, 36, 116, 106, 1;
1, 76, 376, 676, 426, 1;
1, 156, 1056, 2856, 3556, 1706, 1;
1, 316, 2736, 9936, 18536, 17636, 6826, 1;
1, 636, 6736, 30816, 76816, 109416, 84196, 27306, 1;
1, 1276, 16016, 88576, 276896, 526096, 606056, 391396, 109226, 1;
MAPLE
T:= proc(n, k) option remember;
if k=1 and k=n then 1
else 4*T(n-1, k-1) + 2*T(n-1, k)
fi
end: seq(seq(T(n, k), k=1..n), n=1..12); # G. C. Greubel, Nov 18 2019
MATHEMATICA
T[n_, k_]:= T[n, k]= If[k==1 || k==n, 1, 4*T[n-1, k-1] + 2*T[n-1, k]]; Table[T[n, k], {n, 10}, {k, n}]//Flatten (* G. C. Greubel, Nov 18 2019 *)
PROG
(PARI) T(n, k) = if(k==1 || k==n, 1, 4*T(n-1, k-1) + 2*T(n-1, k));
(Magma)
function T(n, k)
if k eq 1 or k eq n then return 1;
else return 4*T(n-1, k-1) + 2*T(n-1, k);
end if;
return T;
end function;
[T(n, k): k in [1..n], n in [1..12]]; // G. C. Greubel, Nov 18 2019
(Sage)
@CachedFunction
def T(n, k):
if (k==1 or k==n): return 1
else: return 4*T(n-1, k-1) + 2*T(n-1, k)
[[T(n, k) for k in (1..n)] for n in (1..12)] # G. C. Greubel, Nov 18 2019
CROSSREFS
KEYWORD
AUTHOR
Zerinvary Lajos, Jun 14 2006
EXTENSIONS
Edited by Don Reble, Jul 24 2006
STATUS
approved