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A191567 Four interlaced 2nd order polynomials: a(4*n)=n*(1+2*n); a(1+2*n)=2*(1+2*n)*(3+2*n); a(2+4*n)=4*(1+n)*(1+2*n). 2
0, 6, 4, 30, 3, 70, 24, 126, 10, 198, 60, 286, 21, 390, 112, 510, 36, 646, 180, 798, 55, 966, 264, 1150, 78, 1350, 364, 1566, 105, 1798, 480, 2046, 136, 2310, 612, 2590, 171 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = T(0,n) and differences T(n,k)=T(n-1,k+1)-T(n-1,k) define the array

0,   6,  4,  30,    3,  70,   24,  126,   10,  198,   60,  286,   21,  390,  ..

6,  -2, 26, -27,   67, -46,  102, -116,  188, -138,  226, -265,  369, -278, ..

-8, 28 -53,  94, -113, 148, -218,  304, -326,  364, -491,  634, -647,  676, ...

T(3,n) mod 9 is the sequence 1, 1, 1, 4, 4, 4, 7, 7, 7, 4, 4, 4 (and periodically repeated with period 12).

A064680(2+n) divides a(n), where b(n) = a(n)/A064680(2+n) = 0, 1, 2, 3, 1, 5, 6, 7, 2,... , n>=0, obeys b(4n)=n and has recurrence b(n)=2*b(n-4)-b(n-8).

LINKS

Table of n, a(n) for n=0..36.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,3,0,0,0,-3,0,0,0,1).

FORMULA

a(n) = 3*a(n-4) - 3*a(n-8) + a(n-12).

a(n)=A061037(n+2) + A181318(n). - Paul Curtz, Jul 19 2011

a(n)=A060819(n) * A145979(n). - Paul Curtz, Sep 06 2011

G.f. x*(-6-4*x-30*x^2-3*x^3-52*x^4-12*x^5-36*x^6-x^7-6*x^8+2*x^10) / ( (x-1)^3 *(1+x)^3 *(x^2+1)^3 ). - R. J. Mathar, Jun 17 2011

Let BEB(n) = a(n)/A061038(n+2) = A060819(n)/A145979(n). Then (BEB(n))^2 = A181318(n)/A061038(n+2) = BEB(n) - A061037(n+2)/A061038(n+2). - Paul Curtz, Jul 19 2011, index corrected by R. J. Mathar, Sep 09 2011

CROSSREFS

Cf. A014105, A000466, A000384, A177427.

Sequence in context: A211945 A121682 A237425 * A274707 A163934 A163939

Adjacent sequences:  A191564 A191565 A191566 * A191568 A191569 A191570

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Jun 12 2011

STATUS

approved

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Last modified December 5 09:15 EST 2016. Contains 278762 sequences.