A160747 -id:A160747 - cp's OEIS frontend

A160788 G.f.: (1+62x+561x^2+1014x^3+449x^4+48*x^5+x^6)/(1-x)^7.

1, 69, 1023, 6761, 28673, 92189, 245463, 570193, 1194577, 2308405, 4180287, 7177017, 11785073, 18634253, 28523447, 42448545, 61632481, 87557413, 121999039, 167063049, 225223713, 299364605, 392821463, 509427185, 653558961

Offset: 0

N. J. A. Sloane, Nov 18 2009

nonn

Source: the De Loera et al. article and the Haws website listed in A160747.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

[89*n^6/30 +151*n^5/15 +56*n^4/3 +19*n^3+371*n^2/30 +74*n/15 +1: n in [0..30]]; // Vincenzo Librandi, Sep 18 2011

CoefficientList[Series[(1 + 62*x + 561*x^2 + 1014*x^3 + 449*x^4 + 48*x^5 + x^6)/(1 - x)^7, {x, 0, 50}], x] (* G. C. Greubel, Apr 26 2018 *)
LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,69,1023,6761,28673,92189,245463},30] (* Harvey P. Dale, Aug 03 2021 *)

x='x+O('x^30); Vec((1+62*x+561*x^2+1014*x^3+449*x^4+48*x^5 +x^6)/(1-x)^7) \\ G. C. Greubel, Apr 26 2018

a(n) = 89*n^6/30 +151*n^5/15 +56*n^4/3 +19*n^3+371*n^2/30 +74*n/15 +1. - R. J. Mathar, Sep 11 2011

A160815 Expansion of (1+62x+562x^2+1023x^3+458x^4+49*x^5+x^6)/(1-x)^7.

Original entry on oeis.org

1, 69, 1024, 6777, 28773, 92589, 246688, 573329, 1201633, 2322805, 4207512, 7225417, 11866869, 18766749, 28730472, 42762145, 62094881, 88223269, 122938000, 168362649, 226992613, 301736205, 395957904, 513523761, 658848961

Offset: 0

N. J. A. Sloane, Nov 18 2009

nonn

Source: the De Loera et al. article and the Haws website listed in A160747.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

[539*n^6/180 +151*n^5/15 +335*n^4/18 +19*n^3 +2231*n^2/180 +74*n/15 +1: n in [0..30]]; // Vincenzo Librandi, Sep 18 2011

CoefficientList[Series[(1+62*x+562*x^2+1023*x^3+458*x^4+49*x^5+x^6)/(1-x)^7, {x, 0, 50}], x] (* G. C. Greubel, Apr 26 2018 *)
LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,69,1024,6777,28773,92589,246688},30] (* Harvey P. Dale, Sep 16 2019 *)

x='x+O('x^30); Vec((1+62*x+562*x^2+1023*x^3+458*x^4+49*x^5 + x^6)/(1-x)^7) \\ G. C. Greubel, Apr 26 2018

a(n) = 539*n^6/180 +151*n^5/15 +335*n^4/18 +19*n^3 +2231*n^2/180 +74*n/15 +1. - R. J. Mathar, Sep 11 2011

A160816 Expansion of (1+62x+563x^2+1032x^3+467x^4+50*x^5+x^6)/(1-x)^7.

Original entry on oeis.org

1, 69, 1025, 6793, 28873, 92989, 247913, 576465, 1208689, 2337205, 4234737, 7273817, 11948665, 18899245, 28937497, 43075745, 62557281, 88889125, 123876961, 169662249, 228761513, 304107805, 399094345, 517620337, 664138961

Offset: 0

N. J. A. Sloane, Nov 18 2009

nonn

Source: the De Loera et al. article and the Haws website listed in A160747.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

[136*n^6/45 +151*n^5/15 +167*n^4/9 +19*n^3+559*n^2/45 +74*n/15 +1: n in [0..30]]; // Vincenzo Librandi, Sep 18 2011

CoefficientList[Series[(1+62*x+563*x^2+1032*x^3+467*x^4 +50*x^5+x^6)/(1-x)^7, {x, 0, 50}], x] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1}, {1, 69, 1025, 6793, 28873, 92989, 247913}, 50] (* G. C. Greubel, Apr 26 2018 *)

x='x+O('x^30); Vec((1+62*x+563*x^2+1032*x^3+467*x^4 +50*x^5 + x^6)/(1-x)^7) \\ G. C. Greubel, Apr 26 2018

a(n) = 136*n^6/45 +151*n^5/15 +167*n^4/9 +19*n^3+559*n^2/45 +74*n/15 +1. - R. J. Mathar, Sep 17 2011

A160817 Expansion of (1+62x+564x^2+1041x^3+476x^4+51*x^5+x^6)/(1-x)^7.

Original entry on oeis.org

1, 69, 1026, 6809, 28973, 93389, 249138, 579601, 1215745, 2351605, 4261962, 7322217, 12030461, 19031741, 29144522, 43389345, 63019681, 89554981, 124815922, 170961849, 230530413, 306479405, 402230786, 521716913, 669428961

Offset: 0

N. J. A. Sloane, Nov 18 2009

nonn

Source: the De Loera et al. article and the Haws website listed in A160747.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

[61*n^6/20 +151*n^5/15 +37*n^4/2 +19*n^3 +249*n^2/20 +74*n/15 +1: n in [0..30]]; // Vincenzo Librandi, Sep 18 2011

CoefficientList[Series[(1+62*x+564*x^2+1041*x^3+476*x^4+51*x^5 +x^6)/(1-x)^7, {x, 0, 50}], x] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1}, {1, 69, 1026, 6809, 28973, 93389, 249138}, 50] (* G. C. Greubel, Apr 26 2018 *)

x='x+O('x^30); Vec((1+62*x+564*x^2+1041*x^3+476*x^4+51*x^5 + x^6)/(1-x)^7) \\ G. C. Greubel, Apr 26 2018

a(n) = 61*n^6/20 +151*n^5/15 +37*n^4/2 +19*n^3 +249*n^2/20 +74*n/15 +1. - R. J. Mathar, Sep 17 2011

A160829 Expansion of (1 + 44x + 337x^2 + 612x^3 + 305x^4 + 40*x^5 + x^6)/(1 - x)^7.

Original entry on oeis.org

1, 51, 673, 4287, 17931, 57321, 152251, 353333, 740077, 1430311, 2590941, 4450051, 7310343, 11563917, 17708391, 26364361, 38294201, 54422203, 75856057, 103909671, 140127331, 186309201, 244538163, 317207997, 407052901, 517178351

Offset: 0

N. J. A. Sloane, Nov 18 2009

nonn

Source: the De Loera et al. article and the Haws website listed in A160747.

G. C. Greubel, Table of n, a(n) for n = 0..10000
J. A. De Loera, D. C. Haws and M. Koppe, Ehrhart Polynomials of Matroid Polytopes and Polymatroids, arXiv:0710.4346 [math.CO], 2007; Discrete Comput. Geom., 42 (2009), 670-702.
Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

[(1/36)*(36 + 174*n + 391*n^2 + 513*n^3 + 442*n^4 + 213*n^5 + 67*n^6): n in [0..30]]; // G. C. Greubel, Apr 28 2018

seq(coeff(series((1+44*x+337*x^2+612*x^3+305*x^4+40*x^5+x^6)/(1-x)^7, x,n+1),x,n),n=0..25); # Muniru A Asiru, Apr 29 2018

LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,51,673,4287,17931,57321, 152251},30] (* or *) CoefficientList[Series[ (1+44x+337x^2+612x^3+ 305x^4+ 40x^5+x^6)/(1-x)^7,{x,0,30}],x] (* Harvey P. Dale, Jun 21 2011 *)

x='x+O('x^99); Vec((1+44*x+337*x^2+612*x^3+305*x^4+40*x^5+x^6)/(1-x)^7) \\ Altug Alkan, Aug 16 2017

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7), with a(0)=1, a(1)=51, a(2)=673, a(3)=4287, a(4)=17931, a(5)=57321, a(6)=152251. - Harvey P. Dale, Jun 21 2011

a(n) = (1/36)*(36 + 174*n + 391*n^2 + 513*n^3 + 442*n^4 + 213*n^5 + 67*n^6). - Harvey P. Dale, Jun 21 2011, corrected by Eric Rowland, Aug 15 2017

A160831 G.f.: (1+62x+570x^2+1095x^3+530x^4+57*x^5+x^6)/(1-x)^7.

Original entry on oeis.org

1, 69, 1032, 6905, 29573, 95789, 256488, 598417, 1258081, 2438005, 4425312, 7612617, 12521237, 19826717, 30386672, 45270945, 65794081, 93550117, 130449688, 178759449, 241143813, 320709005, 421049432, 546296369, 701168961

Offset: 0

N. J. A. Sloane, Nov 18 2009

Source: the De Loera et al. article and the Haws website listed in A160747.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

[193*n^6/60 +151*n^5/15 +109*n^4/6 +19*n^3 +757*n^2/60 +74*n/15 +1: n in [0..30]]; // Vincenzo Librandi, Sep 19 2011

Table[193*n^6/60 +151*n^5/15 +109*n^4/6 +19*n^3 +757*n^2/60 +74*n/15 +1, {n,0,30}] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 69, 1032, 6905, 29573, 95789, 256488}, 30] (* G. C. Greubel, Apr 28 2018 *)

x='x+O('x^30); Vec((1+62*x+570*x^2+1095*x^3+530*x^4+57*x^5 +x^6 )/(1-x)^7) \\ G. C. Greubel, Apr 28 2018

a(n) = 193*n^6/60 +151*n^5/15 +109*n^4/6 +19*n^3 +757*n^2/60 +74*n/15 +1. - R. J. Mathar, Sep 17 2011

A160833 G.f.: (1+62x+569x^2+1086x^3+521x^4+56*x^5+x^6)/(1-x)^7.

Original entry on oeis.org

1, 69, 1031, 6889, 29473, 95389, 255263, 595281, 1251025, 2423605, 4398087, 7564217, 12439441, 19694221, 30179647, 44957345, 65331681, 92884261, 129510727, 177459849, 239374913, 318337405, 417912991, 542199793, 695878961

Offset: 0

N. J. A. Sloane, Nov 18 2009

nonn

Source: the De Loera et al. article and the Haws website listed in A160747.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

[1+n*(n+1)*(287*n^4+619*n^3+1021*n^2+689*n+444)/90: n in [0..30]]; // Vincenzo Librandi, Sep 18 2011

Table[1+n*(n+1)*(287*n^4+619*n^3+1021*n^2+689*n+444)/90, {n,0,30}] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1}, {1, 69, 1031, 6889, 29473, 95389, 255263}, 30] (* G. C. Greubel, Apr 28 2018 *)

for(n=0, 30, print1(1+n*(n+1)*(287*n^4+619*n^3+1021*n^2+689*n +444)/90, ", ")) \\ G. C. Greubel, Apr 28 2018

a(n) = 1+n*(n+1)*(287*n^4+619*n^3+1021*n^2+689*n+444)/90. - R. J. Mathar, Sep 17 2011

A160834 Expansion of: (1+62x+567x^2+1068x^3+503x^4+54*x^5+x^6)/(1-x)^7.

Original entry on oeis.org

1, 69, 1029, 6857, 29273, 94589, 252813, 589009, 1236913, 2394805, 4343637, 7467417, 12275849, 19429229, 29765597, 44330145, 64406881, 91552549, 127632805, 174860649, 235837113, 313594205, 411640109, 534006641, 685298961

Offset: 0

N. J. A. Sloane, Nov 18 2009

nonn

Source: the De Loera et al. article and the Haws website listed in A160747.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

[1+n*(n+1)*(47*n^4+104*n^3+171*n^2+114*n+74)/15: n in [0..30]]; // Vincenzo Librandi, Sep 18 2011

A160834:=n->1+n*(n+1)*(47*n^4+104*n^3+171*n^2+114*n+74)/15: seq(A160834(n), n=0..30); # Wesley Ivan Hurt, Mar 04 2014

Table[1 + n*(n + 1)*(47*n^4 + 104*n^3 + 171*n^2 + 114*n + 74)/15, {n, 0, 30}] (* Wesley Ivan Hurt, Mar 04 2014 *)

for(n=0, 30, print1(1+n*(n+1)*(47*n^4+104*n^3+171*n^2+114*n +74)/15, ", ")) \\ G. C. Greubel, Apr 28 2018

G.f.: (1+62*x+567*x^2+1068*x^3+503*x^4+54*x^5+x^6)/(1-x)^7.
a(n) = 1+n*(n+1)*(47*n^4+104*n^3+171*n^2+114*n+74)/15. - R. J. Mathar, Sep 17 2011
a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7). - Wesley Ivan Hurt, Oct 01 2021

A160835 G.f.: (1+44x+339x^2+630x^3+323x^4+42*x^5+x^6)/(1-x)^7.

Original entry on oeis.org

1, 51, 675, 4319, 18131, 58121, 154701, 359605, 754189, 1459111, 2645391, 4546851, 7473935, 11828909, 18122441, 26991561, 39219001, 55753915, 77733979, 106508871, 143665131, 191052401, 250811045, 325401149, 417632901, 530698351

Offset: 0

N. J. A. Sloane, Nov 18 2009

nonn

Source: the De Loera et al. article and the Haws website listed in A160747.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

[1+n*(n+1)*(23*n^4+48*n^3+98*n^2+73*n+58)/12: n in [0..30]]; // Vincenzo Librandi, Sep 18 2011

Table[1+n*(n+1)*(23*n^4+48*n^3+98*n^2+73*n+58)/12, {n,0,30}] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1}, {1, 51, 675, 4319, 18131, 58121, 154701}, 30] (* G. C. Greubel, Apr 28 2018 *)

for(n=0,30, print1(1+n*(n+1)*(23*n^4+48*n^3+98*n^2+73*n+58)/12, ", ")) \\ G. C. Greubel, Apr 28 2018

a(n) = 1+n*(n+1)*(23*n^4+48*n^3+98*n^2+73*n+58)/12. - R. J. Mathar, Sep 17 2011

A160836 G.f.: (1+62x+565x^2+1050x^3+485x^4+52*x^5+x^6)/(1-x)^7.

Original entry on oeis.org

1, 69, 1027, 6825, 29073, 93789, 250363, 582737, 1222801, 2366005, 4289187, 7370617, 12112257, 19164237, 29351547, 43702945, 63482081, 90220837, 125754883, 172261449, 232299313, 308851005, 405367227, 525813489, 674718961

Offset: 0

N. J. A. Sloane, Nov 18 2009

nonn

Source: the De Loera et al. article and the Haws website listed in A160747.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

[1 +n*(n+1)*(277*n^4+629*n^3+1031*n^2+679*n+444)/90: n in [0..30]]; // Vincenzo Librandi, Sep 18 2011

CoefficientList[Series[(1+62x+565x^2+1050x^3+485x^4+52x^5+x^6)/(1-x)^7, {x,0,30}],x] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,69,1027,6825,29073,93789,250363},30] (* Harvey P. Dale, Sep 01 2015 *)

x='x+O('x^30); Vec((1+62*x+565*x^2+1050*x^3+485*x^4+52*x^5 + x^6)/(1-x)^7) \\ G. C. Greubel, Apr 28 2018

a(n) = 1 +n*(n+1)*(277*n^4+629*n^3+1031*n^2+679*n+444)/90. - R. J. Mathar, Sep 17 2011

a(0)=1, a(1)=69, a(2)=1027, a(3)=6825, a(4)=29073, a(5)=93789, a(6)=250363, a(n)=7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+ 21*a(n-5)- 7*a(n-6)+a(n-7). - Harvey P. Dale, Sep 01 2015

cp's OEIS Frontend

A160788 G.f.: (1+62*x+561*x^2+1014*x^3+449*x^4+48*x^5+x^6)/(1-x)^7.

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A160815 Expansion of (1+62*x+562*x^2+1023*x^3+458*x^4+49*x^5+x^6)/(1-x)^7.

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A160816 Expansion of (1+62*x+563*x^2+1032*x^3+467*x^4+50*x^5+x^6)/(1-x)^7.

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A160817 Expansion of (1+62*x+564*x^2+1041*x^3+476*x^4+51*x^5+x^6)/(1-x)^7.

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A160829 Expansion of (1 + 44*x + 337*x^2 + 612*x^3 + 305*x^4 + 40*x^5 + x^6)/(1 - x)^7.

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A160831 G.f.: (1+62*x+570*x^2+1095*x^3+530*x^4+57*x^5+x^6)/(1-x)^7.

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A160833 G.f.: (1+62*x+569*x^2+1086*x^3+521*x^4+56*x^5+x^6)/(1-x)^7.

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A160834 Expansion of: (1+62*x+567*x^2+1068*x^3+503*x^4+54*x^5+x^6)/(1-x)^7.

A160788 G.f.: (1+62x+561x^2+1014x^3+449x^4+48*x^5+x^6)/(1-x)^7.

A160815 Expansion of (1+62x+562x^2+1023x^3+458x^4+49*x^5+x^6)/(1-x)^7.

A160816 Expansion of (1+62x+563x^2+1032x^3+467x^4+50*x^5+x^6)/(1-x)^7.

A160817 Expansion of (1+62x+564x^2+1041x^3+476x^4+51*x^5+x^6)/(1-x)^7.

A160829 Expansion of (1 + 44x + 337x^2 + 612x^3 + 305x^4 + 40*x^5 + x^6)/(1 - x)^7.

A160831 G.f.: (1+62x+570x^2+1095x^3+530x^4+57*x^5+x^6)/(1-x)^7.

A160833 G.f.: (1+62x+569x^2+1086x^3+521x^4+56*x^5+x^6)/(1-x)^7.

A160834 Expansion of: (1+62x+567x^2+1068x^3+503x^4+54*x^5+x^6)/(1-x)^7.

A160835 G.f.: (1+44x+339x^2+630x^3+323x^4+42*x^5+x^6)/(1-x)^7.

A160836 G.f.: (1+62x+565x^2+1050x^3+485x^4+52*x^5+x^6)/(1-x)^7.