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A119725 Triangular array read by rows: T(n,1) = T(n,n) = 1, T(n,k) = 3*T(n-1,k-1) + 2*T(n-1,k). 6
1, 1, 1, 1, 5, 1, 1, 13, 17, 1, 1, 29, 73, 53, 1, 1, 61, 233, 325, 161, 1, 1, 125, 649, 1349, 1297, 485, 1, 1, 253, 1673, 4645, 6641, 4861, 1457, 1, 1, 509, 4105, 14309, 27217, 29645, 17497, 4373, 1, 1, 1021, 9737, 40933, 97361, 140941, 123929, 61237, 13121, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Second column is like A036563.

Second diagonal is A048473.

LINKS

G. C. Greubel, Rows n = 1..100 of triangle, flattened

Termeszet Vilaga A XI. Természet-Tudomány Diákpályázat díjnyertesei 133.EVF. 6.SZ. jun. 2002. Vegh Lea (and Vegh Erika): Pascal-tipusu haromszogek

EXAMPLE

Triangle begins:

  1;

  1,    1;

  1,    5,    1;

  1,   13,   17,     1;

  1,   29,   73,    53,     1;

  1,   61,  233,   325,   161,      1;

  1,  125,  649,  1349,  1297,    485,      1;

  1,  253, 1673,  4645,  6641,   4861,   1457,     1;

  1,  509, 4105, 14309, 27217,  29645,  17497,  4373,     1;

  1, 1021, 9737, 40933, 97361, 140941, 123929, 61237, 13121, 1;

MAPLE

T:= proc(n, k) option remember;

      if k=1 and k=n then 1

    else 3*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, 3*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, 3*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 3*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 3*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, A036563, A048473, A119726, A119727.

Sequence in context: A299821 A299721 A300342 * A239279 A278880 A111910

Adjacent sequences:  A119722 A119723 A119724 * A119726 A119727 A119728

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 December 6 21:48 EST 2019. Contains 329809 sequences. (Running on oeis4.)