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A176259 A symmetrical triangle based on a recursive sequence sum:a=1; f(n,a)=f(n-1,a)+a*f(n-2,a):t(n,m,a)=f(m + 1, a) + f(n + 1 - m, a) - f(n + 1, a) 0
1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, -1, -1, -1, 1, 1, -2, -3, -3, -2, 1, 1, -4, -6, -7, -6, -4, 1, 1, -7, -11, -13, -13, -11, -7, 1, 1, -12, -19, -23, -24, -23, -19, -12, 1, 1, -20, -32, -39, -42, -42, -39, -32, -20, 1, 1, -33, -53, -65, -71, -73, -71, -65, -53, -33, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,17

COMMENTS

Row sums are:

{1, 2, 2, 2, -1, -8, -25, -60, -130, -264, -515,...}.

LINKS

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

FORMULA

a=1;

f(n,a)=f(n-1,a)+a*f(n-2,a):

t(n,m,a)=f(m + 1, a) + f(n + 1 - m, a) - f(n + 1, a)

EXAMPLE

{1},

{1, 1},

{1, 0, 1},

{1, 0, 0, 1},

{1, -1, -1, -1, 1},

{1, -2, -3, -3, -2, 1},

{1, -4, -6, -7, -6, -4, 1},

{1, -7, -11, -13, -13, -11, -7, 1},

{1, -12, -19, -23, -24, -23, -19, -12, 1},

{1, -20, -32, -39, -42, -42, -39, -32, -20, 1},

{1, -33, -53, -65, -71, -73, -71, -65, -53, -33, 1}

MATHEMATICA

f[0, a_] := 0; f[1, a_] := 1;

f[n_, a_] := f[n, a] = f[n - 1, a] + a*f[n - 2, a];

t[n_, m_, a_] := f[m + 1, a] + f[n + 1 - m, a] - f[n + 1, a];

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

CROSSREFS

Sequence in context: A171414 A270921 A038529 * A132312 A090431 A107336

Adjacent sequences:  A176256 A176257 A176258 * A176260 A176261 A176262

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Apr 13 2010

STATUS

approved

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Last modified February 19 07:51 EST 2019. Contains 320309 sequences. (Running on oeis4.)