A008527 -id:A008527 - cp's OEIS frontend

A008389 Coordination sequence for A_7 lattice.

1, 56, 812, 5768, 26474, 91112, 256508, 623576, 1356194, 2703512, 5025692, 8823080, 14768810, 23744840, 36881420, 55599992, 81659522, 117206264, 164826956, 227605448, 309182762, 413820584, 546468188, 712832792, 919453346

Offset: 0

N. J. A. Sloane and J. H. Conway

T. D. Noe, Table of n, a(n) for n = 0..1000
M. Baake and U. Grimm, Coordination sequences for root lattices and related graphs, arXiv:cond-mat/9706122, 1997; Zeit. f. Kristallographie, 212 (1997), 253-256.
R. Bacher, P. de la Harpe and B. Venkov, Séries de croissance et séries d'Ehrhart associées aux réseaux de racines, C. R. Acad. Sci. Paris, 325 (Series 1) (1997), 1137-1142.
J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Row 7 of A103881.

[1] cat [2 +n^2*(143*n^4 +770*n^2 +707)/30: n in [1..40]]; // G. C. Greubel, May 26 2023

1, seq(2 +n^2*(143*n^4 +770*n^2 +707)/30, n=1..50);

Table[n^2*(143*n^4 +770*n^2 +707)/30 +2 -Boole[n==0], {n,0,40}] (* G. C. Greubel, May 26 2023 *)

[2 +n^2*(143*n^4 +770*n^2 +707)/30 -int(n==0) for n in range(41)] # G. C. Greubel, May 26 2023

G.f.: (1+x)*(1+48*x+393*x^2+832*x^3+393*x^4+48*x^5+x^6)/(1-x)^7. - Colin Barker, Sep 26 2012
a(n) = 2 + n^2*(143*n^4 +770*n^2 +707)/30 with n>0, a(0)=1. - Bruno Berselli, Sep 26 2012
E.g.f.: -1 + (1/30)*(60 +1620*x +10530*x^2 +17490*x^3 +10065*x^4 +2145*x^5 +143*x^6)*exp(x). - G. C. Greubel, May 26 2023

A008399 Coordination sequence for E_6 lattice.

Original entry on oeis.org

1, 72, 1062, 6696, 26316, 77688, 189810, 405720, 785304, 1408104, 2376126, 3816648, 5885028, 8767512, 12684042, 17891064, 24684336, 33401736, 44426070, 58187880, 75168252, 95901624, 120978594, 151048728, 186823368, 229078440, 278657262, 336473352, 403513236

Offset: 0

N. J. A. Sloane and J. H. Conway

M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.

T. D. Noe, Table of n, a(n) for n = 0..1000
M. Baake and U. Grimm, Coordination sequences for root lattices and related graphs, arXiv:cond-mat/9706122, 1997; Zeit. f. Kristallographie, 212 (1997), 253-256.
R. Bacher, P. de la Harpe and B. Venkov, Séries de croissance et séries d'Ehrhart associées aux réseaux de racines, C. R. Acad. Sci. Paris, 325 (Series 1) (1997), 1137-1142.
J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Cf. A008397, A008340, A019557, A019558.

[1] cat [9*n*(13*n^2+7)*(n^2+1)/5: n in [1..40]]; // G. C. Greubel, May 29 2023

1, seq(117/5*n^5+36*n^3+63/5*n, n=1..30);

LinearRecurrence[{6,-15,20,-15,6,-1},{1,72,1062,6696,26316,77688, 189810},30] (* Harvey P. Dale, Oct 24 2022 *)

[9*n*(13*n^2+7)*(n^2+1)//5 +int(n==0) for n in range(41)] # G. C. Greubel, May 29 2023

a(n) = 9*n*(13*n^2+7)*(n^2+1)/5 for n >= 1.
Bacher et al. give a g.f.
G.f.: (1+66*x+645*x^2+1384*x^3+645*x^4+66*x^5+x^6)/(1-x)^6 = 1 + 18*x*(4+35*x+78*x^2+35*x^3+4*x^4)/(1-x)^6. - Colin Barker, Sep 26 2012
E.g.f.: 1 + (1/5)*x*(360 + 2295*x + 3105*x^2 + 1170*x^3 + 117*x^4 )*exp(x). - G. C. Greubel, May 29 2023

A008401 Coordination sequence for {E_6}* lattice.

Original entry on oeis.org

1, 54, 828, 5202, 20376, 60030, 146484, 312858, 605232, 1084806, 1830060, 2938914, 4530888, 6749262, 9763236, 13770090, 18997344, 25704918, 34187292, 44775666, 57840120, 73791774, 93084948

Offset: 0

N. J. A. Sloane

M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.

T. D. Noe, Table of n, a(n) for n = 0..1000
J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Cf. A008402 (partial sums).

[1] cat [6*n*(3*n^4+5*n^2+1): n in [1..40]]; // G. C. Greubel, May 30 2023

Join[{1},Table[18 n^5+30 n^3+6 n,{n,30}]] (* Harvey P. Dale, May 16 2012 *)

[6*n*(3*n^4+5*n^2+1) +int(n==0) for n in range(41)] # G. C. Greubel, May 30 2023

a(n) = 6*n*(3*n^4 + 5*n^2 + 1), n > 0.
G.f.: (1+48*x+519*x^2+1024*x^3+519*x^4+48*x^5+x^6)/(1-x)^6.
E.g.f.: 1 + 6*exp(x)*x*(9 + 60*x + 80*x^2 + 30*x^3 + 3*x^4). - Stefano Spezia, Apr 15 2022

A008402 Crystal ball sequence for {E_6}* lattice.

Original entry on oeis.org

1, 55, 883, 6085, 26461, 86491, 232975, 545833, 1151065, 2235871, 4065931, 7004845, 11535733, 18284995, 28048231, 41818321, 60815665, 86520583, 120707875, 165483541, 223323661, 297115435

Offset: 0

N. J. A. Sloane

M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.

T. D. Noe, Table of n, a(n) for n = 0..1000
J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]
Index entries for crystal ball sequences
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Partial sums of A008401.

[1 +3*n*(n+1)*(n^2+n+1)^2: n in [0..40]]; // G. C. Greubel, May 31 2023

CoefficientList[Series[(1+48x+519x^2+1024x^3+519x^4+48x^5+x^6)/(1-x)^7,{x,0,30}],x] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,55, 883,6085,26461,86491,232975},30] (* Harvey P. Dale, Jun 20 2013 *)

3*n^6+9*n^5+15*n^4+15*n^3+9*n^2+3*n+1 \\ Charles R Greathouse IV, Jun 20 2013

[1 +3*n*(n+1)*(n^2+n+1)^2 for n in range(41)] # G. C. Greubel, May 31 2023

G.f.: (1 + 48*x + 519*x^2 + 1024*x^3 + 519*x^4 + 48*x^5 + x^6)/(1-x)^7.
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); a(0)=1, a(1)=55, a(2)=883, a(3)=6085, a(4)=26461, a(5)=86491, a(6)=232975. - Harvey P. Dale, Jun 20 2013
a(n) = 3*n^6 + 9*n^5 + 15*n^4 + 15*n^3 + 9*n^2 + 3*n + 1 = 1 + 3*n*(n+1)*(n^2+n+1)^2. - Charles R Greathouse IV, Jun 20 2013
E.g.f.: exp(x)*(1 + 54*x + 387*x^2 + 600*x^3 + 300*x^4 + 54*x^5 + 3*x^6). - Stefano Spezia, Apr 15 2022

A008530 Coordination sequence for 4-dimensional primitive di-isohexagonal orthogonal lattice.

Original entry on oeis.org

1, 12, 60, 180, 408, 780, 1332, 2100, 3120, 4428, 6060, 8052, 10440, 13260, 16548, 20340, 24672, 29580, 35100, 41268, 48120, 55692, 64020, 73140, 83088, 93900, 105612, 118260, 131880, 146508, 162180, 178932, 196800, 215820, 236028, 257460, 280152, 304140, 329460, 356148, 384240

Offset: 0

N. J. A. Sloane

Coordination sequence for 4-dimensional cyclotomic lattice Z[zeta_12].

			3*a(5) = 2340 = (2*5+1)^3 + (2*5-1)^3 + (5+1)^3 + (5-1)^3. - _Bruno Berselli_, Jan 31 2013

M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
M. Beck and S. Hosten, Cyclotomic polytopes and growth series of cyclotomic lattices, arXiv:math/0508136 [math.CO], 2005-2006.
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Concatenation([1], List([1..45], n-> 6*n*(1+n^2) )); # G. C. Greubel, Nov 10 2019

[1]cat[6*n^3+6*n: n in [1..45]]; // Vincenzo Librandi, Apr 16 2012

Maple
```
1, seq( 6*k^3+6*k, k=1..45);
```

CoefficientList[Series[(1+4*x+x^2)^2/(1-x)^4,{x,0,45}],x] (* Vincenzo Librandi, Apr 16 2012 *)
LinearRecurrence[{4,-6,4,-1}, {1,12,60,180,408}, 45] (* G. C. Greubel, Nov 10 2019 *)

vector(46, n, if(n==1,1, 6*(n-1)*(1+(n-1)^2)) ) \\ G. C. Greubel, Nov 10 2019

[1]+[6*n*(1+n^2) for n in (1..45)] # G. C. Greubel, Nov 10 2019

G.f.: (1+4*x+x^2)^2/(1-x)^4. - Colin Barker, Apr 14 2012
3*a(n) = (2*n+1)^3 + (2*n-1)^3 + (n+1)^3 + (n-1)^3 for n>0. - Bruno Berselli, Jan 31 2013
E.g.f.: 1 + x*(12 + 18*x + 6*x^2)*exp(x). - G. C. Greubel, Nov 10 2019

A008534 Coordination sequence for {A_6}* lattice.

Original entry on oeis.org

1, 14, 98, 462, 1596, 4410, 10374, 21658, 41272, 73206, 122570, 195734, 300468, 446082, 643566, 905730, 1247344, 1685278, 2238642, 2928926, 3780140, 4818954, 6074838, 7580202, 9370536, 11484550, 13964314, 16855398, 20207012, 24072146, 28507710, 33574674, 39338208, 45867822

Offset: 0

N. J. A. Sloane

Equally, coordination sequence for 6-dimensional cyclotomic lattice Z[zeta_14].

M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
M. Beck and S. Hosten, Cyclotomic polytopes and growth series of cyclotomic lattices, arXiv:math/0508136 [math.CO], 2005-2006.
J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Concatenation([1], List([1..45], n-> 7*n*(6+5*n^2+n^4)/6 )); # G. C. Greubel, Nov 10 2019

[1] cat [7*n*(6+5*n^2+n^4)/6: n in [1..45]]; // G. C. Greubel, Nov 10 2019

1, seq( (7*k^5+35*k^3+42*k)/6, k=1..40);

CoefficientList[Series[(x^6 +8x^5 +29x^4 +64x^3 +29x^2 +8x +1)/(x-1)^6, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 20 2013 *)
Table[If[n==0,1, 7*n*(6+5*n^2+n^4)/6], {n,0,40}] (* G. C. Greubel, Nov 10 2019 *)

vector(46, n, if(n==1,1, 7*(n-1)*(6+5*(n-1)^2+(n-1)^4)/6 ) ) \\ G. C. Greubel, Nov 10 2019

[1]+[7*n*(6+5*n^2+n^4)/6 for n in (1..45)]; # G. C. Greubel, Nov 10 2019

G.f.: (x^6+8*x^5+29*x^4+64*x^3+29*x^2+8*x+1)/(x-1)^6. [Conway-Sloane] - Colin Barker, Sep 21 2012
a(n) = (7/6)*n*(n^2+2)*(n^2+3) for n>0, a(0)=1. - Bruno Berselli, Feb 28 2013
E.g.f.: 1 + x*(84 + 210*x + 210*x^2 + 70*x^3 + 7*x^4)*exp(x)/6. - G. C. Greubel, Nov 10 2019

A008400 Crystal ball sequence for E_6 lattice.

Original entry on oeis.org

1, 73, 1135, 7831, 34147, 111835, 301645, 707365, 1492669, 2900773, 5276899, 9093547, 14978575, 23746087, 36430129, 54321193, 79005529, 112407265, 156833335, 215021215, 290189467, 386091091

Offset: 0

N. J. A. Sloane and J. H. Conway

M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.

T. D. Noe, Table of n, a(n) for n = 0..1000
J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]
Index entries for crystal ball sequences
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

[1 +3*n*(n+1)*(26*n^4 +52*n^3 +73*n^2 +47*n +42)/20: n in [0..40]]; // G. C. Greubel, May 30 2023

seq(39/10*n^6+117/10*n^5+75/4*n^4+18*n^3+267/20*n^2+63/10*n+1, n=0..35);

Table[39/10 n^6+117/10 n^5+75/4 n^4+18n^3+267/20 n^2+63/10 n+1, {n,0, 30}] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,73,1135, 7831,34147,111835,301645},30] (* Harvey P. Dale, Feb 23 2015 *)

a(n)=(78*n^6 + 234*n^5 + 375*n^4 + 360*n^3 + 267*n^2 + 126*n + 20)/20 \\ Charles R Greathouse IV, Feb 10 2017

[1 +3*n*(n+1)*(26*n^4 +52*n^3 +73*n^2 +47*n +42)//20 for n in range(41)] # G. C. Greubel, May 30 2023

a(n) = 1 + (3/20)*n*(n+1)*(26*n^4 + 52*n^3 + 73*n^2 + 47*n + 42).
G.f.: (1+66*x+645*x^2+1384*x^3+645*x^4+66*x^5+x^6)/(1-x)^7. - Colin Barker, Mar 16 2012
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, Feb 23 2015
E.g.f.: (1/20)*(20 + 1440*x + 9900*x^2 + 15480*x^3 + 7785*x^4 + 1404*x^5 + 78*x^6)*exp(x). - G. C. Greubel, May 30 2023

A008529 Coordination sequence for 4-dimensional face-centered cubic orthogonal lattice.

Original entry on oeis.org

1, 14, 68, 202, 456, 870, 1484, 2338, 3472, 4926, 6740, 8954, 11608, 14742, 18396, 22610, 27424, 32878, 39012, 45866, 53480, 61894, 71148, 81282, 92336, 104350, 117364, 131418, 146552, 162806, 180220, 198834, 218688, 239822, 262276, 286090, 311304, 337958, 366092, 395746, 426960

Offset: 0

N. J. A. Sloane

M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Concatenation([1], List([1..45], n-> 2*n*(11 +10*n^2)/3 )); # G. C. Greubel, Nov 09 2019

[1] cat [(20*n^3+22*n)/3: n in [1..45]]; // Vincenzo Librandi, Apr 16 2012

Maple
```
1, seq( (20*k^3+22*k)/3, k=1..45);
```

CoefficientList[Series[(1+x)^2*(1+8*x+x^2)/(1-x)^4,{x,0,45}],x] (* Vincenzo Librandi, Apr 16 2012 *)
Table[If[n==0,1, 2*n*(11 +10*n^2)/3], {n,0,45}] (* or *) LinearRecurrence[{4,-6,4,-1}, {1,14,68,202,456}, 46] (* G. C. Greubel, Nov 09 2019 *)

vector(46, n, if(n==1,1, 2*(n-1)*(11 +10*(n-1)^2)/3) ) \\ G. C. Greubel, Nov 09 2019

[1]+[2*n*(11 +10*n^2)/3 for n in (1..45)]; # G. C. Greubel, Nov 09 2019

G.f.: (1+x)^2*(1+8*x+x^2)/(1-x)^4. - Colin Barker, Apr 14 2012

E.g.f.: 1 + (42 + 60*x^2 + 20*x^3)*exp(x)/3. - G. C. Greubel, Nov 09 2019

A008532 Coordination sequence for 4-dimensional I-centered cubic orthogonal lattice.

Original entry on oeis.org

1, 10, 44, 126, 280, 530, 900, 1414, 2096, 2970, 4060, 5390, 6984, 8866, 11060, 13590, 16480, 19754, 23436, 27550, 32120, 37170, 42724, 48806, 55440, 62650, 70460, 78894, 87976, 97730, 108180, 119350, 131264, 143946, 157420, 171710, 186840, 202834, 219716, 237510

Offset: 0

N. J. A. Sloane

Let f(x) = x^2 + x + 1 then sequence gives f(f(n+1)) - f(f(n)), n >= 0.

Colin Barker, Table of n, a(n) for n = 0..1000
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Concatenation([1], List([1..45], n-> 2*n*(3+2*n^2) )); # G. C. Greubel, Nov 10 2019

[1] cat [2*n*(3+2*n^2): n in [1..45]]; // G. C. Greubel, Nov 10 2019

Maple
```
1, seq( 4*k^3+6*k, k=1..40);
```

Table[If[n==0,1,2*n*(3+2*n^2)], {n,0,40}] (* G. C. Greubel, Nov 10 2019 *)

Vec((x+1)^2*(x^2+4*x+1)/(x-1)^4 + O(x^40)) \\ Colin Barker, Mar 03 2015

vector(46, n, if(n==1,1, 2*(n-1)*(3 +2*(n-1)^2) ) ) \\ G. C. Greubel, Nov 10 2019

[1]+[2*n*(3+2*n^2) for n in (1..45)]; # G. C. Greubel, Nov 10 2019

a(n) = 4*n^3 + 6*n, n >= 1.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4. - Colin Barker, Mar 03 2015
G.f.: (1+x)^2*(1+4*x+x^2)/(1-x)^4. - Colin Barker, Mar 03 2015
a(0) = 1; for n > 0, a(n) = A005898(n-1) + A005898(n) = (n-1)^3 + 2n^3 + (n+1)^3. - Doug Bell, Aug 18 2015
E.g.f.: 1 + 2*x*(5 + 6*x + 2*x^2)*exp(x). - G. C. Greubel, Aug 21 2015

A008533 Coordination sequence for {A_5}* lattice.

Original entry on oeis.org

1, 12, 72, 272, 762, 1752, 3512, 6372, 10722, 17012, 25752, 37512, 52922, 72672, 97512, 128252, 165762, 210972, 264872, 328512, 403002, 489512, 589272, 703572, 833762, 981252, 1147512, 1334072, 1542522, 1774512, 2031752, 2316012, 2629122, 2972972, 3349512

Offset: 0

N. J. A. Sloane

Colin Barker, Table of n, a(n) for n = 0..1000
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Concatenation([1], List([1..45], n-> (4+15*n^2+5*n^4)/2 )); # G. C. Greubel, Nov 10 2019

[1] cat [(4+15*n^2+5*n^4)/2: n in [1..45]]; // G. C. Greubel, Nov 10 2019

Maple
```
1, seq( (5*k^4+15*k^2+4)/2, k=1..40);
```

Table[If[n==0, 1, (4+15*n^2+5*n^4)/2], {n,0,40}] (* G. C. Greubel, Nov 10 2019 *)
LinearRecurrence[{5,-10,10,-5,1},{1,12,72,272,762,1752},50] (* Harvey P. Dale, Jan 08 2020 *)

Vec(-(x+1)*(x^4+6*x^3+16*x^2+6*x+1) / (x-1)^5 + O(x^40)) \\ Colin Barker, Mar 03 2015

vector(46, n, if(n==1,1, (4 +15*(n-1)^2 +5*(n-1)^4)/2 ) ) \\ G. C. Greubel, Nov 10 2019

[1]+[(4+15*n^2+5*n^4)/2 for n in (1..45)]; # G. C. Greubel, Nov 10 2019

a(n) = 5*a(n-1) -10*a(n-2) +10*a(n-3) -5*a(n-4) +a(n-5) for n>5. - Colin Barker, Mar 03 2015
G.f.: (1+x)*(1+6*x+16*x^2+6*x^3+x^4)/(1-x)^5. - Colin Barker, Mar 03 2015
E.g.f.: -1 + (4 + 20*x + 50*x^2 + 30*x^3 + 5*x^4)*exp(x)/2. - G. C. Greubel, Nov 10 2019

cp's OEIS Frontend

A008389 Coordination sequence for A_7 lattice.

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A008399 Coordination sequence for E_6 lattice.

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A008401 Coordination sequence for {E_6}* lattice.

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A008402 Crystal ball sequence for {E_6}* lattice.

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A008530 Coordination sequence for 4-dimensional primitive di-isohexagonal orthogonal lattice.

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A008534 Coordination sequence for {A_6}* lattice.

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