A119727 Triangular array: T(n,k) = T(n,n) = 1, T(n,k) = 5*T(n-1, k-1) + 2*T(n-1, k), read by rows.

1, 1, 1, 1, 7, 1, 1, 19, 37, 1, 1, 43, 169, 187, 1, 1, 91, 553, 1219, 937, 1, 1, 187, 1561, 5203, 7969, 4687, 1, 1, 379, 4057, 18211, 41953, 49219, 23437, 1, 1, 763, 10009, 56707, 174961, 308203, 292969, 117187, 1, 1, 1531, 23833, 163459, 633457, 1491211, 2126953, 1699219, 585937, 1

Offset

1,5

Comments

Second column is A048488. Second diagonal is A057651.

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,    7,     1;
  1,   19,    37,      1;
  1,   43,   169,    187,      1;
  1,   91,   553,   1219,    937,       1;
  1,  187,  1561,   5203,   7969,    4687,       1;
  1,  379,  4057,  18211,  41953,   49219,   23437,       1;
  1,  763, 10009,  56707, 174961,  308203,  292969,  117187,      1;
  1, 1531, 23833, 163459, 633457, 1491211, 2126953, 1699219, 585937, 1;

Maple

T:= proc(n, k) option remember;
      if k=1 and k=n then 1
    else 5*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, 5*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, 5*T(n-1, k-1) + 2*T(n-1, k)); \\ G. C. Greubel, Nov 18 2019
(Magma)
function T(n, k)
  if k eq 1 or k eq n then return 1;
  else return 5*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 5*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, A048488, A057651, A119725, A119726.

Sequence in context: A176284 A154233 A174033 * A157272 A176200 A046739

Adjacent sequences: A119724 A119725 A119726 * A119728 A119729 A119730

Keyword

easy,nonn,tabl

Author

Zerinvary Lajos, Jun 14 2006

Extensions

Edited by Don Reble, Jul 24 2006

Status

approved