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A176242 Triangle generated by T(n,k) = q^k*T(n-1, k) + T(n-1, k-1), with q=2. 2
1, 1, 1, 1, 5, 1, 1, 21, 13, 1, 1, 85, 125, 29, 1, 1, 341, 1085, 589, 61, 1, 1, 1365, 9021, 10509, 2541, 125, 1, 1, 5461, 73533, 177165, 91821, 10541, 253, 1, 1, 21845, 593725, 2908173, 3115437, 766445, 42925, 509, 1, 1, 87381, 4771645, 47124493, 102602157, 52167917, 6260845, 173229, 1021, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row sums are: {1, 2, 7, 36, 241, 2078, 23563, 358776, 7449061, 213188690, ...}.

REFERENCES

Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), page 176

LINKS

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

FORMULA

T(n,k) = T(n-1, k-1) + q^k*T(n-1, k), with q=2.

EXAMPLE

Triangle begins as:

  1;

  1,     1;

  1,     5,      1;

  1,    21,     13,       1;

  1,    85,    125,      29,       1;

  1,   341,   1085,     589,      61,      1;

  1,  1365,   9021,   10509,    2541,    125,     1;

  1,  5461,  73533,  177165,   91821,  10541,   253,   1;

  1, 21845, 593725, 2908173, 3115437, 766445, 42925, 509, 1;

MAPLE

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

    q:=2;

      if k=1 or k=n then 1

    else T(n-1, k-1) + q^k*T(n-1, k)

      fi; end:

seq(seq(T(n, k), k=1..n), n=1..12); # G. C. Greubel, Nov 22 2019

MATHEMATICA

q:=2; T[n_, k_]:= T[n, k]= If[k==1 || k==n, 1, q^k*T[n-1, k] + T[n-1, k-1]]; Table[T[n, k], {n, 12}, {k, n}]//Flatten (* modified by G. C. Greubel, Nov 22 2019 *)

PROG

(PARI) T(n, k) = my(q=2); if(k==1 || k==n, 1, q^k*T(n-1, k) + T(n-1, k-1)); \\ G. C. Greubel, Nov 22 2019

(MAGMA)

function T(n, k)

  q:=2;

  if k eq 1 or k eq n then return 1;

  else return T(n-1, k-1) + q^k*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 22 2019

(Sage)

@CachedFunction

def T(n, k):

    q=2;

    if (k==1 or k==n): return 1

    else: return q^k*T(n-1, k) + T(n-1, k-1)

[[T(n, k) for k in (1..n)] for n in (1..12)] # G. C. Greubel, Nov 22 2019

CROSSREFS

Cf. this sequence (q=2), A176243 (q=3), A176244 (q=4).

Sequence in context: A047909 A171243 A111577 * A036969 A080249 A333143

Adjacent sequences:  A176239 A176240 A176241 * A176243 A176244 A176245

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Apr 12 2010

EXTENSIONS

Edited by G. C. Greubel, Nov 22 2019

STATUS

approved

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Last modified July 4 09:26 EDT 2020. Contains 335446 sequences. (Running on oeis4.)