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A202551 Triangle T(n,k), read by rows, given by (1, -1, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. 1
1, 1, -1, 0, -1, 1, -1, 1, 1, -1, -1, 3, -2, -1, 1, 0, 2, -5, 3, 1, -1, 1, -2, -2, 7, -4, -1, 1, 1, -5, 7, 1, -9, 5, 1, -1, 0, -3, 12, -15, 1, 11, -6, -1, 1, -1, 3, 3, -21, 26, -4, -13, 7, 1, -1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,12

COMMENTS

Riordan array (1/(1-x+x^2), x*(x-1)/(1-x+x^2)).

LINKS

Table of n, a(n) for n=0..54.

FORMULA

T(n,k) = T(n-1,k) + T(n-2,k-1) - T(n-1,k-1) - T(n-2,k).

G.f.: 1/(1+(y-1)*x+(1-y)*x^2).

Sum_{k, 0<=k<=n} T(n,k)*x^k = A190873(n+1), A190871(n+1), A057086(n), A057085(n+1), A057084(n), A030240(n), A030192(n), A030191(n), A001787(n+1), A057083(n), A099087(n), A010892(n), A000007(n), (-1)^n*A000045(n+1) for x = -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2 respectively.

EXAMPLE

Triangle begins :

1

1, -1

0, -1, 1

-1, 1, 1, -1

-1, 3, -2, -1, 1

0, 2, -5, 3, 1, -1

CROSSREFS

Cf. A129267, A199324

Sequence in context: A206713 A096874 A090046 * A129267 A199324 A287576

Adjacent sequences:  A202548 A202549 A202550 * A202552 A202553 A202554

KEYWORD

sign,tabl

AUTHOR

Philippe Deléham, Dec 21 2011

STATUS

approved

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Last modified April 19 11:26 EDT 2021. Contains 343113 sequences. (Running on oeis4.)