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A145561

Alternating row sums of triangle A049029 (S2(5)).
(history; published version)

#8 by Bruno Berselli at Thu Jul 27 04:25:58 EDT 2017

STATUS

reviewed

approved

#7 by Joerg Arndt at Thu Jul 27 04:12:37 EDT 2017

STATUS

proposed

reviewed

#6 by Michel Marcus at Wed Jul 26 12:41:24 EDT 2017

STATUS

editing

proposed

#5 by Michel Marcus at Wed Jul 26 12:41:17 EDT 2017

FORMULA

a(n) = Sum_{m=sum(1..n} (-1)^(m+1)*A049029(n,m),m=1..n), n>=1.

a(n) = y(n), where y(0) = -1, y(1) = 1, y(2) = 4, y(3) = 31, y(4) = 359, and -32*k*(1 + k)*(1 + 2 k)*(1 + 4 k)*(3 + 4 k)*y(k) + (1679 + 5920 k + 8080 k^2 + 5120 k^3 + 1280 k^4)*y(k+1) + (-2550 - 4580 k - 2880 k^2 - 640 k^3)*y(k+2) + (675 + 640 k + 160 k^2)*y(k+3) + (-50 - 20 k)*y(k+4) + y(k+5) = 0. - _Benedict W. J. Irwin_, Jul 12 2017

y(0) = -1, y(1) = 1, y(2) = 4, y(3) = 31, y(4) = 359,

-32*k*(1 + k)*(1 + 2 k)*(1 + 4 k)*(3 + 4 k)*y(k) + (1679 + 5920 k + 8080 k^2 + 5120 k^3 + 1280 k^4)*y(k+1) + (-2550 - 4580 k - 2880 k^2 - 640 k^3)*y(k+2) + (675 + 640 k + 160 k^2)*y(k+3) + (-50 - 20 k)*y(k+4) + y(k+5) = 0. - Benedict W. J. Irwin, Jul 12 2017

CROSSREFS

Cf. A049120 (row sums).

AUTHOR

Wolfdieter Lang , Oct 17 2008

STATUS

proposed

editing

#4 by Benedict W. J. Irwin at Wed Jul 26 12:37:55 EDT 2017

STATUS

editing

proposed

#3 by Benedict W. J. Irwin at Wed Jul 12 06:02:32 EDT 2017

FORMULA

a(n)=y(n), where

y(0) = -1, y(1) = 1, y(2) = 4, y(3) = 31, y(4) = 359,

MATHEMATICA

Table[DifferenceRoot[Function[{y, k}, {-32 k (1 + k) (1 + 2 k) (1 + 4 k) (3 + 4 k) y[k] + (1679 + 5920 k + 8080 k^2 + 5120 k^3 + 1280 k^4) y[1 + k] + (-2550 - 4580 k - 2880 k^2 - 640 k^3) y[2 + k] + (675 + 640 k + 160 k^2) y[3 + k] + (-50 - 20 k) y[4 + k] + y[5 + k] == 0, y[0] == -1, y[1] == 1, y[2] == 4, y[3] == 31, y[4] == 359}]][n], {n, 1, 20}] (* Benedict W. J. Irwin, Jul 12 2017 *)

STATUS

approved

editing

Discussion

Wed Jul 19

13:47

OEIS Server: This sequence has not been edited or commented on for a week
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#2 by Russ Cox at Sat Mar 31 13:20:18 EDT 2012

AUTHOR

_Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) _ Oct 17 2008

Discussion

Sat Mar 31

13:20

OEIS Server: https://oeis.org/edit/global/878

#1 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009

NAME

Alternating row sums of triangle A049029 (S2(5)).

DATA

1, 4, 31, 359, 5546, 107249, 2492701, 67693534, 2103854581, 73651161959, 2868077514776, 122980857764819, 5758029769553101, 292305762924889804, 15992593021331060611, 938143525674896325299, 58739433900424758545186, 3910020681156059085488189

OFFSET

1,2

FORMULA

a(n)=sum((-1)^(m+1)*A049029(n,m),m=1..n), n>=1.

E.g.f.: (from Jabotinsky structure): 1-exp(1-1/(1-4*x)^(1/4)).

CROSSREFS

A049120 (row sums).

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Oct 17 2008

STATUS

approved