A119726 Triangular array read by rows: T(n,1) = T(n,n) = 1, T(n,k) = 4*T(n-1, k-1) + 2*T(n-1, k).

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

Offset

1,5

Comments

Second column is A048487.

Second diagonal is A020989.

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

Cf. A007318, A020989, A048483, A048487, A119725, A119727, A123208.

Sequence in context: A296963 A176560 A152602 * A103999 A154985 A157275

Adjacent sequences: A119723 A119724 A119725 * A119727 A119728 A119729

Keyword

easy,nonn,tabl

Author

Zerinvary Lajos, Jun 14 2006

Extensions

Edited by Don Reble, Jul 24 2006

Status

approved