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

Author

Zerinvary Lajos, Jun 14 2006

Keywords

• easy
• nonn
• tabl

Comments

Second column is A048488. Second diagonal is A057651.

Examples

			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;
		

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

Crossrefs

Cf. A007318, A048488, A057651, A119725, A119726.

Programs

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

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 *)

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

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

Extensions

Edited by Don Reble, Jul 24 2006