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A174096 A symmetrical triangle sequence as polynomial coefficients as q-form sum:q=2;t(n,k)=If[n == 0 || n == 1, 1, Binomial[n - k + 1, k] + Binomial[k + 1, (n - k)]] 0
1, 1, 1, 1, 12, 1, 1, 12, 12, 1, 1, 12, 16, 12, 1, 1, 13, 17, 17, 13, 1, 1, 16, 36, 32, 36, 16, 1, 1, 17, 49, 37, 37, 49, 17, 1, 1, 32, 93, 92, 36, 92, 93, 32, 1, 1, 33, 124, 197, 80, 80, 197, 124, 33, 1, 1, 36, 204, 304, 197, 44, 197, 304, 204, 36, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 14, 26, 42, 62, 138, 208, 472, 870, 1528,...}.

LINKS

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

FORMULA

q=2;

t(n,k)=If[n == 0 || n == 1, 1, Binomial[n - k + 1, k] + Binomial[k + 1, (n - k)]];

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

EXAMPLE

{1},

{1, 1},

{1, 12, 1},

{1, 12, 12, 1},

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

{1, 13, 17, 17, 13, 1},

{1, 16, 36, 32, 36, 16, 1},

{1, 17, 49, 37, 37, 49, 17, 1},

{1, 32, 93, 92, 36, 92, 93, 32, 1},

{1, 33, 124, 197, 80, 80, 197, 124, 33, 1},

{1, 36, 204, 304, 197, 44, 197, 304, 204, 36, 1}

MATHEMATICA

f[n_, k_] = If[n == 0 || n == 1, 1, Binomial[n - k + 1, k] + Binomial[k + 1, (n - k)]];

a=Table[CoefficientList[Sum[f[n, k]*x^k, {k, 0, n}], x], {n, 0, 10}];

b[q_] := Sum[q^i*Floor[a/2^i], {i, 0, 10}];

Table[Flatten[b[q]], {q, 1, 10}]

CROSSREFS

Cf. A011973

Sequence in context: A058306 A010207 A010206 * A070636 A168646 A051457

Adjacent sequences:  A174093 A174094 A174095 * A174097 A174098 A174099

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Mar 07 2010

STATUS

approved

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Last modified February 18 15:30 EST 2020. Contains 332019 sequences. (Running on oeis4.)