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A174097 A symmetrical triangle sequence as polynomial coefficients as q-form sum:q=3;t(n,k)=If[n == 0 || n == 1, 1, Binomial[n - k + 1, k] + Binomial[k + 1, (n - k)]] 0
1, 1, 1, 1, 19, 1, 1, 19, 19, 1, 1, 19, 24, 19, 1, 1, 20, 25, 25, 20, 1, 1, 24, 70, 65, 70, 24, 1, 1, 25, 90, 71, 71, 90, 25, 1, 1, 65, 231, 230, 70, 230, 231, 65, 1, 1, 66, 295, 671, 211, 211, 671, 295, 66, 1, 1, 70, 684, 941, 671, 84, 671, 941, 684, 70, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 21, 40, 64, 92, 255, 374, 1124, 2488, 4818,...}.

LINKS

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

FORMULA

q=3;

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, 19, 1},

{1, 19, 19, 1},

{1, 19, 24, 19, 1},

{1, 20, 25, 25, 20, 1},

{1, 24, 70, 65, 70, 24, 1},

{1, 25, 90, 71, 71, 90, 25, 1},

{1, 65, 231, 230, 70, 230, 231, 65, 1},

{1, 66, 295, 671, 211, 211, 671, 295, 66, 1},

{1, 70, 684, 941, 671, 84, 671, 941, 684, 70, 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: A040363 A040362 A040361 * A174040 A176078 A022182

Adjacent sequences:  A174094 A174095 A174096 * A174098 A174099 A174100

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.)