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A159681 The general form of the recurrences are the a(j), b(j) and n(j) solutions of the 2 equations problem: 5*n(j)+1=a(j)*a(j) and 7*n(j)+1=b(j)*b(j) with positiv integer numbers. +0
2
0, 24, 3432, 487344, 69199440, 9825833160, 1395199109304, 198108447688032, 28130004372591264, 3994262512460271480, 567157146764985958920, 80532320578115545895184, 11435022364945642531157232 (list; graph; listen)
OFFSET

1,2

FORMULA

The a(j) recurrence is a(1)=1; a(2)=11; a(t+2)=12*a(t+1)-a(t)

resulting in terms 1, 11, 131, 1561

The b(j) recurrence is b(1)=1; b(2)=13; b(t+2)=12*b(t+1)-b(t)

resulting in terms 1, 13, 155, 1847

The n(j) recurrence is n(0)=n(1)=0; n(2)=24; n(t+3)=143*(n(t+2)-n(t+1))+n(t)

resulting in terms 0, 0, 24, 3432, 487344 as listed above

G.f.: -24*x^2/((x-1)*(x^2-142*x+1)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 20 2009]

MAPLE

for a from 1 by 2 to 100000 do b:=sqrt((7*a*a-2)/5): if (trunc(b)=b) then

n:=(a*a-1)/5: La:=[op(La), a]:Lb:=[op(Lb), b]:Ln:=[op(Ln), n]: end if: end do:

CROSSREFS

A157456, A077417, A077416

Sequence in context: A001512 A088731 A072529 this_sequence A071639 A061530 A166768

Adjacent sequences: A159678 A159679 A159680 this_sequence A159682 A159683 A159684

KEYWORD

nonn

AUTHOR

Paul Weisenhorn (paulweisenhorn(AT)online.de), Apr 19 2009

EXTENSIONS

More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 20 2009

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Last modified December 2 11:54 EST 2009. Contains 167921 sequences.


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