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A174037 A triangle sequence of the form:q=2:t(n,m,q)=Sum[q^i*Floor[Binomial[n, m]/2^i], {i, 0, 10}] 0
1, 1, 1, 1, 4, 1, 1, 5, 5, 1, 1, 12, 16, 12, 1, 1, 13, 36, 36, 13, 1, 1, 16, 49, 92, 49, 16, 1, 1, 17, 93, 197, 197, 93, 17, 1, 1, 32, 124, 304, 464, 304, 124, 32, 1, 1, 33, 204, 540, 768, 768, 540, 204, 33, 1, 1, 36, 237, 752, 1556, 1788, 1556, 752, 237, 36, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 6, 12, 42, 100, 224, 616, 1386, 3092, 6952,...}.

LINKS

Table of n, a(n) for n=0..65.

FORMULA

q=2:

t(n,m,q)=Sum[q^i*Floor[Binomial[n, m]/2^i], {i, 0, 10}]

EXAMPLE

{1},

{1, 1},

{1, 4, 1},

{1, 5, 5, 1},

{1, 12, 16, 12, 1},

{1, 13, 36, 36, 13, 1},

{1, 16, 49, 92, 49, 16, 1},

{1, 17, 93, 197, 197, 93, 17, 1},

{1, 32, 124, 304, 464, 304, 124, 32, 1},

{1, 33, 204, 540, 768, 768, 540, 204, 33, 1},

{1, 36, 237, 752, 1556, 1788, 1556, 752, 237, 36, 1}

MATHEMATICA

t[n_, m_, q_] = Sum[q^i*Floor[Binomial[n, m]/2^i], {i, 0, 10}];

Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 1, 10}]

CROSSREFS

Sequence in context: A136489 A166455 A171142 * A173077 A131239 A114033

Adjacent sequences:  A174034 A174035 A174036 * A174038 A174039 A174040

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Mar 06 2010

STATUS

approved

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Last modified July 18 07:10 EDT 2019. Contains 325134 sequences. (Running on oeis4.)