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A115523 Number of ordered quadruples (i,j,k,l) in range [0..n] satisfying i == j mod 2, j == k mod 3 and k == l mod 4. 1
1, 2, 5, 12, 33, 60, 111, 176, 287, 440, 637, 864, 1237, 1652, 2147, 2752, 3555, 4428, 5517, 6700, 8177, 9878, 11785, 13824, 16441, 19214, 22265, 25676, 29685, 33900, 38715, 43776, 49595, 55964, 62821, 69984, 78445, 87248, 96647, 106800, 118167, 129948, 142905, 156332 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Quasipolynomial of order 12. - Charles R Greathouse IV, Dec 03 2014

LINKS

Table of n, a(n) for n=0..43.

Index entries for linear recurrences with constant coefficients, signature (1,0,1,0,-1,0,-1,1,0,0,0,2,-2,0,-2,0,2,0,2,-2,0,0,0,-1,1,0,1,0,-1,0,-1,1).

FORMULA

a(n) = binomial(n+1,4) - presumably quadratic (PORC) correction term which depends on n mod 24.

From Charles R Greathouse IV, Dec 03 2014: (Start)

n = 0 mod 12: a(n) = (n^4 + 4*n^3 + 12*n^2 + 24*n + 24)/24

n = 1 mod 12: a(n) = (n^4 + 4*n^3 + 12*n^2 + 20*n + 11)/24

n = 2 mod 12: a(n) = (n^4 + 4*n^3 + 10*n^2 + 12*n + 8)/24

n = 3 mod 12: a(n) = (n^4 + 4*n^3 + 8*n^2 + 8*n + 3)/24

n = 4 mod 12: a(n) = (n^4 + 4*n^3 + 12*n^2 + 20*n + 8)/24

n = 5 mod 12: a(n) = (n^4 + 4*n^3 + 10*n^2 + 12*n + 5)/24

n = 6 mod 12: a(n) = (n^4 + 4*n^3 + 12*n^2 + 12*n)/24

n = 7 mod 12: a(n) = (n^4 + 4*n^3 + 8*n^2 + 8*n + 3)/24

n = 8 mod 12: a(n) = (n^4 + 4*n^3 + 10*n^2 + 12*n + 8)/24

n = 9 mod 12: a(n) = (n^4 + 4*n^3 + 12*n^2 + 12*n + 3)/24

n = 10 mod 12: a(n) = (n^4 + 4*n^3 + 12*n^2 + 8*n + 8)/24

n = 11 mod 12: a(n) = (n^4 + 4*n^3 + 6*n^2 + 4*n + 1)/24

(End)

a(n) = (19958400*(n^4+4*n^3+12*n^2+24*n+24) - (1235*n^2+2*1127*n+215)*m^11 +(74987*n^2+2*69047*n+13541)*m^10 -(1983300*n^2+2*1844700*n+377520)*m^9 +(29983800*n^2+2*28201800*n+6115890)*m^8 - (285731655*n^2+2*272034411*n+63415275)*m^7 +(1784142591*n^2+2*1720539051*n+436295013)*m^6 -(7344548530*n^2+2*7175131810*n+1995595030)*m^5 +(19515989350*n^2+2*19301456350*n+5911801060)*m^4 -(31672473360*n^2+2*31658103312*n+10685562360)*m^3 +(27907182072*n^2+2*28127231352*n+10490664096)*m^2 -(9932634720*n^2+2*10110299040*n+4359398400)*m)/479001600 where m=n-12*floor(n/12). - Luce ETIENNE, Sep 27 2017

PROG

(PARI) a(n)=my(s); for(i=0, n, forstep(j=i%2, n, 2, forstep(k=j%3, n, 3, s+=(n-(k%4))\4+1))); s \\ naive; Charles R Greathouse IV, Dec 03 2014

CROSSREFS

Cf. A115520.

A010881.

Sequence in context: A014326 A148284 A148285 * A176336 A010843 A084075

Adjacent sequences:  A115520 A115521 A115522 * A115524 A115525 A115526

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane and Vinay Vaishampayan, Mar 09 2006

STATUS

approved

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Last modified August 2 11:23 EDT 2021. Contains 346422 sequences. (Running on oeis4.)