A088943 -id:A088943 - cp's OEIS frontend

A088941 a(n)=12sum(1<=i<=j<=k<=n,ij/k).

0, 12, 54, 154, 349, 685, 1217, 2009, 3134, 4674, 6720, 9372, 12739, 16939, 22099, 28355, 35852, 44744, 55194, 67374, 81465, 97657, 116149, 137149, 160874, 187550, 217412, 250704, 287679, 328599, 373735, 423367, 477784, 537284, 602174, 672770

Offset: 0

Benoit Cloitre, Oct 25 2003

Always an integer.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Cf. A088942, A088943.

A051798(n) - 1.

LinearRecurrence[{5,-10,10,-5,1},{0,12,54,154,349},40] (* Harvey P. Dale, May 01 2014 *)

a(n)=if(n<0,0,a(n)=n/24*(9*n^3 + 58*n^2 + 123*n + 98))

a(n)=(n/24)*(9*n^3 + 58*n^2 + 123*n + 98).

G.f.: x*(x^3-4*x^2+6*x-12) / (x-1)^5. - Colin Barker, Jun 15 2013

A088942 a(n)=60sum(1<=i<=j<=k<=n,i^2j/k).

Original entry on oeis.org

0, 60, 390, 1450, 4045, 9421, 19361, 36281, 63326, 104466, 164592, 249612, 366547, 523627, 730387, 997763, 1338188, 1765688, 2295978, 2946558, 3736809, 4688089, 5823829, 7169629, 8753354, 10605230, 12757940, 15246720, 18109455, 21386775

Offset: 0

Benoit Cloitre, Oct 25 2003

Always an integer. Can be expressed as a polynomial with rational coefficients of degree 5.

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Cf. A088941, A088943.

a(n)=60*sum(k=1,n,sum(j=1,k,sum(i=1,j,i^2*j/k)))

a(n) = n/120 * (96n^4 + 765n^3 + 2210n^2 + 2275n + 1354).

G.f.: x*(x^4-5*x^3+10*x^2+30*x+60) / (x-1)^6. - Colin Barker, Jun 15 2013

A088944 a(n) = least k such that for any m>=0 ksum(1<=u<=v<=w<=m,u^nv/w) is an integer.

Original entry on oeis.org

6, 12, 60, 60, 84, 84, 60, 60, 132, 132, 5460, 5460, 12, 12, 1020, 1020, 1596, 1596, 660, 660, 276, 276, 5460, 5460, 12, 12, 60, 60, 28644, 28644, 1020, 1020

Offset: 0

Benoit Cloitre, Oct 25 2003

nonn

Cf. A088941, A088942, A088943, A088945.

for n>=1 a(2n+1)=a(2n)

A088945 a(n) =60sum(1<=u<=v<=w<=m,u^2v^2/w).

Original entry on oeis.org

0, 60, 690, 3630, 13035, 37059, 89839, 193879, 382834, 704694, 1225368, 2032668, 3240693, 4994613, 7475853, 10907677, 15561172, 21761632, 29895342, 40416762, 53856111, 70827351, 92036571, 118290771, 150507046, 189722170, 237102580

Offset: 0

Benoit Cloitre, Oct 25 2003

Always an integer. Can be expressed as a polynomial with rational coefficients of degree 6.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Cf. A088941, A088942, A088943, A088944.

LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,60,690,3630,13035,37059,89839},30] (* Harvey P. Dale, Mar 20 2024 *)

n*(200*n^5+1752*n^4+5705*n^3+8370*n^2+5075*n+498)/360. - Vladeta Jovovic, Oct 27 2003

G.f.: -x*(x^5-6*x^4+15*x^3+60*x^2+270*x+60) / (x-1)^7. - Colin Barker, Jun 19 2013

cp's OEIS Frontend

A088941 a(n)=12sum(1<=i<=j<=k<=n,ij/k).

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A088942 a(n)=60sum(1<=i<=j<=k<=n,i^2j/k).

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A088944 a(n) = least k such that for any m>=0 ksum(1<=u<=v<=w<=m,u^nv/w) is an integer.

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Author

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Formula

A088945 a(n) =60sum(1<=u<=v<=w<=m,u^2v^2/w).

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Author

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cp's OEIS Frontend

A088941 a(n)=12*sum(1<=i<=j<=k<=n,i*j/k).

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Mathematica

PARI

Formula

A088942 a(n)=60*sum(1<=i<=j<=k<=n,i^2*j/k).

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PARI

Formula

A088944 a(n) = least k such that for any m>=0 k*sum(1<=u<=v<=w<=m,u^n*v/w) is an integer.

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Formula

A088945 a(n) =60*sum(1<=u<=v<=w<=m,u^2*v^2/w).

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Author

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Programs

Mathematica

Formula

A088941 a(n)=12sum(1<=i<=j<=k<=n,ij/k).

A088942 a(n)=60sum(1<=i<=j<=k<=n,i^2j/k).

A088944 a(n) = least k such that for any m>=0 ksum(1<=u<=v<=w<=m,u^nv/w) is an integer.

A088945 a(n) =60sum(1<=u<=v<=w<=m,u^2v^2/w).