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A114619 2*A079291 (twice squares of Pell numbers). 2
0, 2, 8, 50, 288, 1682, 9800, 57122, 332928, 1940450, 11309768, 65918162, 384199200, 2239277042, 13051463048, 76069501250, 443365544448, 2584123765442, 15061377048200, 87784138523762, 511643454094368 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Cross-referenced sequences A116484, A001109, A108475, A090390 are also generated by A*B given in the program code.

LINKS

Table of n, a(n) for n=0..20.

FORMULA

G.f. 2*x*(1-x)/((x+1)*(x^2-6*x+1))

a(n) = ( ( (1-Sqrt[ 2 ])^n + (1+Sqrt[ 2 ])^n) /2)^2 + (-1)^(n+1). The formula (1-Sqrt[ 2 ])^n + (1+Sqrt[ 2 ])^n) /2) is the that given by Reinhard Zumkeller in A001333. Furthermore, ( ( (A001333)_(n) )^2 + ( (A114619)_(n) )^2 - 1)^(1/2) = A001542_(n) and ( 2*A001542_(n) + 1)^(1/2) = A001333_(2n) - Antonio Pane (apane1(AT)spc.edu), Dec 15 2007

PROG

Floretion Algebra Multiplication Program, FAMP Code: 1jbasejseq[A*B] with A = - .5'i + .5'j - .5i' + .5j' + 'kk' - .5'ik' - .5'jk' - .5'ki' - .5'kj' and B = - .5'j + .5'k - .5j' + .5k' - 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki' ; apart from initial term.

CROSSREFS

Cf. A116484, A001109, A108475, A090390.

Cf. A079291, A001333, A001542.

Sequence in context: A136226 A046165 A227264 * A027047 A034491 A231352

Adjacent sequences:  A114616 A114617 A114618 * A114620 A114621 A114622

KEYWORD

easy,nonn

AUTHOR

Creighton Dement, Feb 17 2006

STATUS

approved

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Last modified December 7 12:17 EST 2021. Contains 349581 sequences. (Running on oeis4.)