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A193554 Triangle read by rows: first column: top entry is 1, then powers of 2; rest of triangle is Pascal's triangle A007318. 3
1, 1, 1, 2, 1, 1, 4, 1, 2, 1, 8, 1, 3, 3, 1, 16, 1, 4, 6, 4, 1, 32, 1, 5, 10, 10, 5, 1, 64, 1, 6, 15, 20, 15, 6, 1, 128, 1, 7, 21, 35, 35, 21, 7, 1, 256, 1, 8, 28, 56, 70, 56, 28, 8, 1, 512, 1, 9, 36, 84, 126, 126, 84, 36, 9, 1, 1024, 1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1, 2048, 1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The original definition of A135233 made no sense. In fact A135233 is the binomial transform of the present sequence.

LINKS

G. C. Greubel, Rows n = 0..100 of triangle, flattened

EXAMPLE

Triangle begins:

1;

1, 1;

2, 1, 1;

4, 1, 2, 1;

8, 1, 3, 3, 1;

16, 1, 4, 6, 4, 1;

32, 1, 5, 10, 10, 5, 1;

64, 1, 6, 15, 20, 15, 6, 1;

...

MAPLE

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

if k=n then 1

elif k=0 then 2^(n-1)

else binomial(n-1, k-1)

fi; end:

seq(seq(T(n, k), k=0..n), n=0..12); # G. C. Greubel, Nov 20 2019

MATHEMATICA

T[n_, k_]:= T[n, k]= If[k==n, 1, If[k==0, 2^(n-1), Binomial[n-1, k-1]]];

Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Nov 20 2019 *)

PROG

(PARI) T(n, k) = if(k==n, 1, if(k==0, 2^(n-1), binomial(n-1, k-1) )); \\ G. C. Greubel, Nov 20 2019

(Magma)

function T(n, k)

if k eq n then return 1;

elif k eq 0 then return 2^(n-1);

else return Binomial(n-1, k-1);

end if; return T; end function;

[T(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Nov 20 2019

(Sage)

@CachedFunction

def T(n, k):

if (k==n): return 1

elif (k==0): return 2^(n-1)

else: return binomial(n-1, k-1)

[[T(n, k) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Nov 20 2019

CROSSREFS

Cf. A000079 (row sums)

Cf. A007318, A135233.

Sequence in context: A199856 A301906 A302150 * A131350 A131087 A105475

Adjacent sequences: A193551 A193552 A193553 * A193555 A193556 A193557

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Jul 30 2011

STATUS

approved

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Last modified December 8 03:48 EST 2022. Contains 358672 sequences. (Running on oeis4.)