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, 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

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