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A174095 A symmetrical triangle sequence as polynomial coefficients as q-form sum:q=1;t(n,k)=If[n == 0 || n == 1, 1, Binomial[n - k + 1, k] + Binomial[k + 1, (n - k)]] 0
1, 1, 1, 1, 7, 1, 1, 7, 7, 1, 1, 7, 10, 7, 1, 1, 8, 11, 11, 8, 1, 1, 10, 18, 15, 18, 10, 1, 1, 11, 26, 19, 19, 26, 11, 1, 1, 15, 39, 38, 18, 38, 39, 15, 1, 1, 16, 53, 67, 31, 31, 67, 53, 16, 1, 1, 18, 70, 109, 67, 22, 67, 109, 70, 18, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 9, 16, 26, 40, 73, 114, 204, 336, 552,...}.

LINKS

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

FORMULA

q=1;

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, 7, 1},

{1, 7, 7, 1},

{1, 7, 10, 7, 1},

{1, 8, 11, 11, 8, 1},

{1, 10, 18, 15, 18, 10, 1},

{1, 11, 26, 19, 19, 26, 11, 1},

{1, 15, 39, 38, 18, 38, 39, 15, 1},

{1, 16, 53, 67, 31, 31, 67, 53, 16, 1},

{1, 18, 70, 109, 67, 22, 67, 109, 70, 18, 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: A019620 A105395 A120437 * A305607 A229779 A050179

Adjacent sequences:  A174092 A174093 A174094 * A174096 A174097 A174098

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.)