cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A156934 G.f. of the z^1 coefficients of the FP2 in the second column of the A156925 matrix.

Original entry on oeis.org

1, 8, 38, 144, 487, 1552, 4796, 14592, 44061, 132568, 398210, 1195280, 3586659, 10760992, 32284216, 96854144, 290564217, 871694760, 2615086750, 7845263120, 23535792671, 70607381808
Offset: 1

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Author

Johannes W. Meijer, Feb 20 2009

Keywords

Crossrefs

Equals second column of A156925
Other columns A156935, A156936, A156937

Formula

a(n)=6*a(n-1)-12*a(n-2)+10*a(n-3)-3*a(n-4)+2
a(n)=7*a(n-1)-18*a(n-2)+22*a(n-3)-13*a(n-4)+3*a(n-5)
a(n):= -1/6*n^3-n^2-7/3*n-9/4+9/4*3^n
G.f.: GF4(z;m=1) = z*(1+z)/((1-3*z)*(1-z)^4)

A156935 G.f. of the z^2 coefficients of the FP2 in the third column of the A156925 matrix.

Original entry on oeis.org

-11, -108, -425, 720, 25678, 255048, 1901298, 12339600, 73794315, 418519612, 2289264465, 12207642976, 63925371180, 330387702160, 1691454191604, 8600517968736, 43516016460465, 219401923888740
Offset: 2

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Author

Johannes W. Meijer, Feb 20 2009

Keywords

Crossrefs

Equals third column of A156925
Other columns A156934, A156936, A156937

Formula

a(n)=24*a(n-1)-254*a(n-2)+1568*a(n-3)-6291*a(n-4)+17296*a(n-5)- 33460*a(n-6)+45984*a(n-7)-44663*a(n-8)+29976*a(n-9)-13230*a(n-10)+3456*a(n-11)-405*a(n-12)
a(n)= 75/32+101/24*n-225/16*3^n+375/32*5^n+289/72*n^2-1/8*3^(1+n)*n^3-9/4*3^n*(n)^2- 15/2*3^n*n+19/8*n^3+ 61/72*n^4+1/6*n^5+1/72*n^6
G.f.: GF4(z;m=2) = z^2*(-11+156*z-627*z^2+736*z^3+591*z^4-1116*z^5-369*z^6)/((1-z)^7*(1-3*z)^4*(1-5*z))

A156936 G.f. of the z^3 coefficients of the FP2 in the fourth column of the A156925 matrix.

Original entry on oeis.org

-6, -242, -7382, -130472, -1594852, -15166900, -119173924, -788897224, -4270968154, -15821839894, 13226522262, 1056215331024, 14319250065624, 147391347765784, 1340374086462424
Offset: 2

Views

Author

Johannes W. Meijer, Feb 20 2009

Keywords

Crossrefs

Cf. A156933.
Equals fourth column of A156925.
Other columns A156934, A156935, A156937.

Formula

a(n) = 58*a(n-1) - 1571*a(n-2) + 26428*a(n-3)- 309755*a(n-4) + 2689810*a(n-5) - 17964865*a(n-6) + 94564560*a(n-7) - 398823930*a(n-8) + 1362709780*a(n-9) - 3799420462*a(n-10) + 8679603176*a(n-11) - 16269149542*a(n-12) + 24993226196*a(n-13) - 31349144530*a(n-14) + 31885547728*a(n-15) - 26017270869*a(n-16) + 16759251378*a(n-17) - 8320633119*a(n-18) + 3068440380*a(n-19) - 790800975*a(n-20) + 127028250*a(n-21) - 9568125*a(n-22).
G.f.: GF4(z;m=3) = z^2*(-6 + 106*z - 2772*z^2 + 76070*z^3 - 1087552*z^4 + 8632650*z^5 - 40358780*z^6 + 106452214*z^7 - 99774996*z^8 - 284430514*z^9 + 1125952500*z^10 - 1581820542*z^11 + 737716032*z^12 + 414532350*z^13 - 357790500*z^14 - 81870750*z^15 - 1275750*z^16)/((1-z)^10*(1-3*z)^7*(1-5*z)^4*(1-7*z)).

A156937 G.f. of the z^4 coefficients of the FP2 in the fifth column of the A156925 matrix.

Original entry on oeis.org

839, 48451, 1277794, 20499983, 217367668, 1310255037, -3988076346, -248575701031, -4423141531241, -58198384719342, -649357370614484, -6449481786729030, -58156975255481312
Offset: 3

Views

Author

Johannes W. Meijer, Feb 20 2009

Keywords

Crossrefs

Cf. A156933.
Equals fifth column A156925.
Other columns A156934, A156935, A156936.

Formula

G.f.: GF4(z;m=4) = z^3*(839 - 48034*z + 1020994*z^2 - 6315109*z^3 - 125732218*z^4 + 2906593672*z^5 - 19318662264*z^6 - 132970633714*z^7 + 4088983763169*z^8 - 44795079122946*z^9 + 308476276414274*z^10 - 1459296681369171*z^11 + 4631899460241844*z^12 - 7747445435417248*z^13 - 9002247331934848*z^14 + 106298680448237476*z^15 - 371569253030465479*z^16 + 786920087358011162*z^17 - 1036342589202760506*z^18 + 621638121199512933*z^19 + 473980516442576550*z^20 - 1356311903948266536*z^21 + 1141880919093176760*z^22 -255315553951597650*z^23 - 197701524871970625*z^24 + 83458617238946250*z^25 + 18532381423893750*z^26 + 519742224421875*z^27)/((1-z)^13*(1-3*z)^10*(1-5*z)^7*(1-7*z)^4*(1-9*z)).
Previous Showing 11-14 of 14 results.