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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. 4
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)